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greetings welcome to electronic circuits

my name is behzod Razavi and i will be

your guide on an interesting journey

through the world of electronics as you

know electronics has affected our lives

in many different respects and today we

can see it everywhere and our objective

foundation for analysis and design of

electronic circuits today what I would

like to accomplish is first give you an

introduction to electronics and then

start with semiconductor physics the

devices that we use in electronic design

are based on semiconductors and to

understand how the devices operate we

need to understand semiconductor physics

so for that we'll go over some general

concepts that are familiar to you from

physics and chemistry and then we will

look at the concept of doping as one

method that we use in semiconductor

devices all right so before we go there

let's just take a look at what we

learned in basic circuit theory and what

we are hoping to learn in this course so

all right well in basic circuit theory

we learned of course circuit theorems

KVL and KCl and Norton equivalent dan7

an equivalent etc but we also had a few

devices a few components that we could

play with resistors capacitors inductors

maybe transformers but they were very

few in number so we had only resistors

capacitors and inductors so this is what

we call what we would say basic electric

and with such a small number of

components especially only two terminal

devices is very difficult to build many

useful and exciting circuits so if you

recall from your circuit Theory courses

they didn't really have that many

applications from real life examples of

a circuit design another hand in

electronics the world is different so in

electronics in addition to these basic

components we have some other components

that suddenly open up the horizons for

circuit design we have for example

diodes of course we don't know what they

transistors we have two types of

transistors and MOS transistors and then

we also have what we call op amps you

might have seen them as a black box

before so an op amp looks like this is

an amplifier with two inputs so with so

many devices available suddenly we can

sophisticated circuits and that's why

electronics is so exciting we every day

we come up with new ideas view new ways

of connecting these things together you

can imagine how many combinations and

permutations of these devices can exist

and that's why it is interesting to

study electronics all right now but

because these devices are based on

semiconductors we do need to understand

semiconductor physics to some extent

just the way a an engineer designing an

automobile needs to know how the engine

operates or the carburetor operates

everything else we also need to know how

the this device or that device operates

internally so for that we start we have

to start with semiconductor physics the

semiconductor physics that we cover here

is not as deep as what you would see in

horses but it's just barely enough for

this course it's a little boring for the

next one or two lectures but you have to

bear with me so that you understand this

stuff and then you can move on to more

exciting circuit examples etc alright so

now based on these we can figure out

what topics we will cover in this course

so the outline of this course is like

this we start with semiconductor physics

which is the foundation for all of these

semiconductor physics at a simple level

and once we understand that we can go

ahead and build each of these devices so

we go ahead and build a diode and

understand its inner workings and more

importantly find out how we can model

this we remember that a resistor

satisfies Ohm's law we remember the

capacitor satisfies AI is equal to C DV

over DT how about a diode what model

what mathematical expression should be

use for the diode and once we know that

we can go and build circuits out of

diodes so we learn about diodes and then

are these useful absolutely you have

them everywhere you have them in your

charger that charges your cell phone you

have them in your laptop everywhere so

it's good to know how diode circuits

operate our event will repeat this for

these other devices so we go to for

example bipolar transistors and once we

know how they operate on how we can

model them we can go ahead and build

circuits out of these transistors so you

don't bipolar circuits and finally for

most devices so we go to mosque

transistors and after understanding

their operation and they're modeling we

can build Maus circuits at the end of

this course we will also look at

circuits that incorporate our pumps in

them and perform interesting functions

so at the end of the course we'll also

look at what I call often based circuits

and this will take us about forty-five

hours of lectures okay all right so with

this we now have a clear picture as to

where we will start and where we will

end and we're going to start with

semiconductor physics trying to

understand how what a semiconductor is

what it means and then how we can modify

it again we can play with it etc until

we can build a diode from that that is

the objective as we go along in this

course we will also have what I call the

frontiers in electronics series the

purpose of frontiers in electronics is

to give you examples of applications of

electronics in daily life this helps us

appreciate the beauty of electronic

circuits and also see how what we learn

in this course becomes useful in

everything that we see out there today

so we have many examples of electronic

for example cell phones and GPS and

Wi-Fi etc today we will spend a little

bit of time on the cell phone itself and

see how it might operate our treatment

is very simple and the level of our

understanding in electronic circuits one

we're not pretending that we can design

a cell phone or we can even repair a

cell phone we're just trying to

understand how it generally might

I'm not for me of a cell phone so we

would like to see what exactly is going

on inside the cell phone when our voice

or data is communicated from one place

to another place wirelessly now our

treatment is at a simple level so we

functionality that we would have in such

a system well a cell phone would consist

of a transmitter to transmit the data or

voice or video of interest and a

receiver to receive that processor and

information okay so what do we need to

build a wireless transmitter well first

we need an antenna so let's pick an

antenna here that's the symbol for an

antenna which takes an electrical signal

and converts it to an electromagnetic

signal so that the waves can propagate

through the air and get to the receiver

all right now we have let's say my voice

which goes to microphone so here's a

microphone mic and the microphone

generates an electrical signal so if I

plot that as a function of time it looks

like this so that's what we get at the

microphone so the question is can I just

connect the microphone output due

directly to the antenna and let it

convert the to electromagnetic waves and

sell them out so can I just short this

from here to here now of course you may

say well the microphone signal is very

weak so you should probably amplify it

before you do anything with it so that's

true so let's put an amplifier here this

is just a very simple audio amplifier to

amplify the signal that's generated by

these microphones typically these swings

that you would see at the output here or

on the other of a few millivolts maybe

10 millivolts so we would need to

amplify them but can i still can I go

ahead and connect this point at this

point well no and the reason for that is

that for an antenna to be a good antenna

electromagnetic energy its dimensions

however they are whether is round or

rectangular etc its dimensions must be

comparable to the wavelength of the

signal that we apply to it so for

if you consider this transmitter that is

transmitter has small antenna inside we

don't see it this transmitter operates

at I don't know 500 megahertz 600

megahertz the antenna is about this size

and somewhere inside or maybe a loop or

something all right so we need a

wavelength that is reasonable in terms

of these antenna dimensions on the other

hand the signal that is produced by the

microphone the audio signal the voice

signal has a frequency range of 20 Hertz

to 20 kilohertz and if you do a quick

calculation you will see that the

wavelength associated with these

frequencies is extremely large so

there's just no way that we could

connect and how do you signal directly

to an antenna and hope that antenna with

any reasonable dimensions would be able

to radiate it would not radiate so what

do we do here well what we should think

of is start out with a frequency that is

friendly to the antenna so maybe one

gigahertz two gigahertz whatever we want

in cellphones we have 900 megahertz we

have 1.8 gigahertz 2 gigahertz 2.2

gigahertz so something like that so we

start out with a frequency that is good

for the antenna so here's a frequency I

will just say 1 gigahertz as an example

1 gigahertz and what you're hoping that

is that this information can be somehow

combined with this frequency so that

this frequency this waveform carries

this information for us and then the

result is applied to the antenna is the

frequency high enough that the internal

dimensions will be reasonable and

everything is good so we call this

it will carry the information that we

would like to transmit so this is called

a carrier all right now how do we

combine this information with this in

other words how do we impress this

information upon this carrier well you

can imagine we can change the amplitude

according to this information or the

frequency etc so there would be some

sort of change or modulation as we call

it in the properties of this carrier

according to the signal that is produced

by the microphone so that calls for some

box which we call the modulator so

here's the modulator and the job of the

modulator is to take the information

signal that we are producing from the

microphone from a camera etc and take

this carrier combine these somehow and

give us a result that has this

information on top of the signal okay

all right now this is ready to be

transmitted the frequency of the signal

is high enough and I say 1 gigahertz

that the antenna would be reasonable of

visible dimensions but if you are hoping

to transmit this information over a long

range let's say a mile or two miles or

two kilometres etcetera then we might

want to apply a large amount of power to

this antenna and for that we need

another amplifier placed between the

modulator and the antenna and this is

called a power amplifier so here we have

APA it's a cellphone might transmit 500

milliwatts even a watt at this point so

that goes a long range alright so we see

most of the blocks that we would need

some sort of processing of the audio

signal a modulator a power amplifier now

this carrier has to come from somewhere

it's a periodic signal so we may think

of an oscillator as a circuit that

produces a periodic signal it oscillates

so it keeps producing a sine or a cosine

or a square wave or something so this

will come from an oscillator so you may

have a 1 gigahertz oscillator or a two

kickers oscillator and the signal comes

here this is called the carrier signal

sometimes we call it the local

oscillator and then we somehow impress

this information on this maybe modulate

this amplitude or its face or its

frequency and then we go through the

power and when we come out all right

that's the most basic transmitter that

we can build okay now let's go to the

receive side and see what should happen

there we sort of expect the reverse of

all of this to happen right so let's see

what what we need to do there okay I

will draw the transmitter receiver on

this side these waves propagate through

the air and are picked up by my receiver

antenna so I have an antenna here and

I'm trying to build my receiver so

here's the receiver so I guess I should

and by the time the waves get to my

receiver they are actually quite

attenuated so this way will be very

little by the time it gets here if it's

a long distance and the signal that

comes in so is so small that it can't do

much with it so that calls for

amplification so we need an amplifier

right here which we call a low noise

amplifier and lnaa and now the signal is

a little bigger so we can play with it

and then we have to go through some

processing maybe demodulation or

whatever it takes so that at the end we

retrieve this original signal so I'm

hoping that now in my receiver I take

back that on your signal I can apply to

speaker and I can listen to it so there

will be some processing here I know this

is vague but in the interest of time I

won't go through the details of this

processing and then here eventually we

give the signal to a speaker and that

produces the audio signal back for us

this is the journey that the voice

signal takes has thoughts from this

microphone goes through the air is

received by the receiver and processed

to generate the the voice signal you can

imagine that there are many other

building blocks in here that we are not

talking about in a cell phone today we

have a lot a great deal more complexity

that than what we see here but this is

the bare bone structure at all of our

understanding that helps us appreciate

what we have here so we see some

functions that are very good and

we have amplification and the files here

here here maybe more down here we have

oscillations to build an oscillator we

application so we have some sort of

amplification that is converted to an

there are also some interesting

functions inside here inside here that

we are not covering at this point very

well let's begin with semiconductor

physics and we start with some general

concepts so let's begin with our general

concepts okay well we know that atoms

consist of a nucleus and some electrons

surrounding the atom and of interest to

us this is the nucleus and there are

electrons in the in these various shells

or as we call them orbitals and of

interest to us is or the electrons in

the last outer shell of the atom so we

have some electrons in the last shell or

in the last orbital and these electrons

play an interesting role in how these

atoms interact with other atoms all

right so these electrons out here

electron they're called valence

the ones in the last orbital the

outermost shell different atoms have

different number of electrons in their

valence among their valence electrons so

as an example we have sodium sodium has

only one electron in the outermost shell

and as a result is very reactive it was

to get rid of that electron as soon as

possible so sodium reacts with

everything else very quickly then we

has eight electrons and that means that

this orbital is last orbital is complete

so it has no tendency to interact with

anything else but we call a noble gas so

it has no interaction all right and then

we have for example silicon and silicon

happens to have four electrons in its

outermost shell four electrons so

silicon is not as reactive as sodium or

as inert as nonreactive as neon is

so it could interact with other atoms to

some extent and this is the foundation

for semiconductors that we study in this

course all right so that's silicon atom

and let's try to do this let's try to

build what we call a crystal of silicon

a crystal of silicon is a very regular

array of silicon atoms placed very

so here's how it goes do we have the

silicon atom here another silicon atom

here another one here and so on so you

have another one here another one here

etc this silicon atom has four electrons

available in its outermost shell so what

it does it begins to share these

electrons with the neighboring atoms so

now this silicon but some of the time

has eight electrons so it's complete

because it has four of its own and then

its borrowing for from these four

neighboring atoms and so on this

continues everywhere these bonds are

so you can see that this is a very

regular and clean array of atoms very

organized and that's what we call the

crystal or we call a lattice so silicon

has the ability to do this with proper

processing of silicon we can create

silicon crystal and that's so what we

use in semiconductor physics all right

so let's say that I have a piece of

silicon that I bought and it has the

structure in it and I'm wondering if

this can conduct electricity so I come

along and I apply connected contact here

contact here a piece of wire on each

side and I connect the battery here with

some voltage v1 let's say 1 volt or 2

volts or something and I'm curious to

see if there's any current flowing

through the semiconductors all right

well for the current to flow we need

some sort of maybe electron to flow some

sort of charge carrier to flow so we

need perhaps an electron to start from

here and travel all the way this way

going from the positive end to the

negative end so we need an electron do

we have an electron available here that

can take off and go around and carry

charge it seems that the electrons are

all occupied they're all bound to these

atoms it seems that no electron is free

this electron is shared between these

two this electrons are shared between

these two etc in fact if we perform this

test at Absolute Zero that is exactly

true an absolute zero these electrons

are all connected these atoms that have

have no way to go but at any finite

temperature because of the ambient

energy that we have the thermal energy

that we have once in a while one of

these electrons comes off from that bond

and is available to move around so

statically speaking at any temperature

drones are free because they just come

off come off of these bonds so this

might instead of this we may have an a

free electron that becomes available and

now yes if we apply voltage some of

these free electrons can conduct

electricity around this loop also a

piece of silicon can conduct electricity

at a finite temperature let's say at the

room temperature and for that reason we

call it a semi conductor is not as good

as metals which are very good conductors

right and it's not as bad as for example

diamond which is a an insulator it

doesn't conduct it's somewhere in

between it conducts to some extent and

that's why we call it a semi conductors

very well so that's what we have for the

crystal and the silicon the piece of

silicon okay so in this study we need to

answer a number of questions as we go

along understand these principles

so let me write these questions here and

we will try to answer these questions

one by one as we go through the physics

of semiconductors so let's add a page

okay so we are dealing with currents and

voltages in semiconductors currents are

carried when an electron for example

moves around or generally a charge

carrier moves around so the first

question is where do charge carriers

come from so let's write that down here

where do Sarge carriers come from well I

just mentioned that in a piece of

silicon we do have electrons charge

carriers at a finite temperature because

of the thermal energy once in a while

the lecture the electron inside the atom

inside the valence band has enough

energy to come off and become a free

electron but is that the only type of

charge carrier maybe there are other

types of charge carriers that will come

along as well so for the second question

that we want to answer in our studies is

what types of charge carriers do we have

the most familiar to us are electrons

but are they electrons the only types

that can conduct a current through a

piece of semiconductor or any other

piece of material so we would like to

okay so then once we understand these

two we need to go and ask the following

question how can we modify density of

intuitively we know that if in a

material we have lots of carriers then

that material is very conductive if you

have very few carriers is not very

conductive so that's what we call the

density of carriers now if I give you a

piece of silicon and it has some number

of electrons per cubic centimeters or

cubic meter and you're not happy with

that number you want to increase it or

decrease it how do we exactly do that

how do we make sure that this piece of

silicon has a higher number of free

electrons available for current

conduction or a lower number of Korus

electrons available so that's what we

call modification of carrier densities

so we'd like to see how that works

and last question that we need to answer

in relation to semiconductors is how do

charge carriers move that seems the

logical question right because we are

interested in how current is created in

a semiconductor so if I say these

electrons are going from here to here by

what mechanism are they exactly moving

and we need to understand and be able to

quantify that mechanism so we will look

at that at some point all right so we

have partially answered this question we

saw that electrons are freed from the

bonds inside the silicon crystal but

there are other interesting questions

that we need to answer so let's go and

try them one by one all right so I need

to introduce another concept that is

necessary for us to understand these

questions so let's talk about that

concept for a few minutes and then we go

back to these questions in the meantime

I go to a new color so this is what we

what happened here okay I call it

concept of and gap energy now along the

lines of what we just discussed about a

piece of silicon and some free electrons

that we can find there here's what we

would expect let's try to plot as a

function of absolute temperature the

density of free electrons in silicon

just very qualitatively so this is

density of free electrons in silicon

this means that if I go take a piece of

silicon either some temperature room

temperature for example and I go and

look at one cubic centimeter and I count

how many free electrons we have that

would be any value here all right so as

I said at Absolute Zero we have nothing

so at Absolute Zero everything is frozen

we have no carriers available and

generally what we know is that as

temperature goes up more electrons have

a chance to break free because of the

higher available thermal energy in the

ambient so in the ambience so we have to

have some behavior like this now where

there is linear non-linear we don't know

at this point but it has some sort of

behavior it's if we know that it has to

increase with temperature okay so that's

fine but something interesting happens

if we study two different types of

elements for example let's say this is

for silicon silicon has 4 electrons in

its outermost shell and it has this type

now if I go to the periodic table I can

find another element that also has four

electrons in its outermost shell and

that's germanium so for germanium if I

try to construct the same plot I will

so that's germanium both of these are in

the same column in the periodic table

semiconductors all right so what is it

like this wise germanium density of free

electrons a stronger function of

density okay so we are hoping that maybe

there's one equation that can describe

both of these and there's only one

number in there that depends on silicon

or germanium right and in fact that

equation exists so we'll try to write an

equation for this behavior so his model

right will write the density of

electrons we denote that by n n is the

number of electrons per cubic centimeter

and then we'll write ah this is called

for an intrinsic piece of silicon we

don't know why it's called intrinsic at

this point but don't worry butter we'll

see that later so intrinsic silicon and

N is the density of electrons the number

of electrons per cubic centimeter so

there's a nice equation for this that

gives us this behavior so let me write

it's 5.2 times 10 to the 15 times T to

the power of three halves times

exponential alpha minus EG over 2k t

all right so let me walk you through

these we have some number times the

absolute temperature to the power of

three over two multiplied by this

exponential this exponential has

something here which we call the bandgap

energy so this is called deep and gap

energy and what it really means is the

amount of energy that an electron needs

let's say in silicon to break free from

the bond inside the atom and become

available for current conduction so

that's the amount of energy we need and

this immediately tells us something it

says that in silicon we need a higher

energy we need a higher temperature to

give the same amount of the same number

of electrons per cubic centimeter as

germanium so that means that eg is

higher for silicon than for germanium

now K is Boltzmann's constant both man's

constant and its value is good to

memorize you'll encounter this many

times in electronics is equal to one

point three eight times ten to the minus

twenty three jewels over Kelvin and T is

absolute temperature okay so what we see

is that this equation applies to both

germanium and silicon the only

difference is that eg has different

values for different elements so let me

write that here eg is approximately

equal to one point one two the unit is a

little strange you might remember this

the unit of energy is electron volts

similar to joules but this is more

convenient electron volts that Rambo's

means the amount of energy that we need

to take one electron across one volt of

voltage difference and this is for

silicon and then for germanium is lower

seven electron volts or germanium so

that tells us why we have a stronger

function here for germanium than for

silicon all right and then finally if

you're curious for example for diamond

is 2.5 electron volts for diamond and

that's why diamond is such a good

insulator as for diamond this would be

way down here because of this

exponential relationship so diamond has

very very low current through it so it's

considered a good insulator all right

now with this in hand we can go ahead

and look at a an example so let me use

these equations to just give you an

example so here's an example for silicon

let's go ahead and calculate an I so at

t equals 300 kelvin we have an i equals

so we go place 300 here EG is one point

one two electron volts we have to worry

about these units etc k is this much T

is 303 calculations and an eye comes out

to be approximately 10 to the 10

electrons per cubic centimeter these are

the number of free electrons that we

have at the room temperature so if we

take a 1 cube 1 1 centimeter by positive

it was centimeters the piece of silicon

silicon Cristal as I showed you before

right so this is one cubic centimeter

then inside here we have 10 to the 10

okay so that gives us a feel for what

kind of electron density or conductivity

we might have in a piece of silicon at

the room temperature or not this number

10 to the 10 electrons per cubic

centimeter doesn't have too much

significance for us we don't know if

this is a large number or small number

or what so somehow we have to compare

this to something else we don't know if

this is a is this considered a really

good conductor because we have 10 to the

10 electrons in one cubic centimeter or

well you we have to remember how many

atoms of silicon we have in one cubic

centimeter and that number is the

following so 5 times 10 to the 22

silicon atoms per cubic centimeter so in

this little piece here we have this many

atoms and of those only this many

electrons have been freed so if you look

at the ratio of these two we see that a

very very small percentage of the atoms

of silicon have actually released an

electron with this thermal energy that's

available all right so that's why we say

this is a semiconductor we don't have an

abundance of electrons for current

conduction the ratio of these two is 10

five thousand five times ten to the

twelve is a huge number so a very very

small fraction of the atoms have

released an electron so a piece of

silicon as I have described it so far is

a roughly poor conductor because we

don't have that many electrons available

all right so we'll say a poor conductor

to conduct but not as much as we would

like it so what I have described so far

is called pure silicon or more precisely

is called intrinsic silicon so a piece

of silicon the way we describe it just a

bunch of silicon atoms next to each

other is called pure silicon also known

as in trinsic silicon okay these have

the same meaning if you want to call it

pure that's fine it's just pure it's

just all silicon atoms in a nice array

in the crystal all right so now we need

to address or familiarize ourselves with

one more concept before all of these

come together and that's the concept of

holes so a lot let's talk about that

this is something that you probably have

not seen in any courses before because

this is so specific to semiconductors

all right so what are holes well let's

change the color of our pin and see what

we can do okay so let's again take a

piece of silicon we the way we have seen

it at some finite temperature and

observe the following so let's say we

had a silicon piece of silicon here

lfyou silicon atoms and so on and it

just happens that this bond loses one

electron because of the thermal energy

one action came out of here and started

moving around so the void that is left

behind is called the hole so there's a

hole here because there used to be an

electron here but it's gone so this bond

is missing an electron and that's what

we call the hole so this we call the

all right so because the electron has

negative charge when it's taken away

this hole has positive charge all right

so we associate positive charge two

holes in the amount that we associate

negative charge two electrons okay but

something interesting happens so let's

say that I have this piece of silicon

I take a picture of it at time zero and

I see the situation a an electron has

just come out of this and a hole has

appeared okay all right now a little

later I take another picture and this is

what I observe so we just take the same

piece of silicon we have these atoms

sitting here and what I see is that a

little lighter so let's say T equals T

one maybe a nanosecond later or maybe a

second later doesn't really matter for

us what I see is that one electron has

come out of this bond here and fill this

hole here so now the hole is here

reiben know that everyone is capable of

relinquishing an electron if there's

enough thermal energy and just happens

that this bond lost an electron and the

selection of fell into this hole

completed this bond and now we have a

hole here okay so we have a hole here

now let's take another picture a little

later and see what happens so we go to T

equals T 2 and try the same thing so

again we have these atoms silicon here

so they come here and so on and all of

these and it just happens that another

electron comes out of this bond and

fills this hole so we have this complete

but then we have a hole here alright so

in three consecutive pictures that we

took we saw that these electrons were

coming off of their bonds and fill in

these holes or equivalently what we can

say is that there was one hole and that

hole moved from left to right it moved

from here to here and then to here and

because a hole has positive charge

associated with it we can say that

positive charge has traveled from the

left side of the semiconductor to the

right side as we look at it at different

points in time so we can say a current

has crew hasn't has been created as we

go from here to here so we say holes are

capable of conducting current just the

way electrons are and that's a very

important concept so when you remember

this question that we raised how where

the charge carriers come from well we

have electrons that we also have holes

and these two are two different entities

that can simultaneously conduct current

electrons can move and conduct current

holes can move and conduct current all

right if holes go from left to right we

have positive current going from left to

right if electrons go from left to right

we have negative current going from left

to right so that's something to remember

I also want to emphasize that conduction

by holes is not the same as conduction

by electrons so let me raise the

why are poles slower than electrons okay

as we will see later when we give

properties to electrons and holes we say

holes are slower maybe I factor of two

why is that well you can see here that

the way this hole moved was actually by

electrons being is released and trapped

one electron was released from here and

trapped here then another electron was

released from here from here and trapped

here so it's not like an electron that

just shoots through the lattice and

conducts current is the this operation

of release and trap release and trap of

electrons that equivalently allows a

hole to move around and this trap in

this release and trap process is slower

than just an electron moving on its own

without interacting with the other atoms

so we say that whole movement of holes

is based on release and trap mechanisms

and that's why it is slower than the

movement of electrons all right so

that's what we have so far and now we

need to look at a few other interesting

concepts remember that I had this

equation for the number of free

electrons in a piece of silicon at a

given temperature how many free holes do

I have available as well it's the same

number because if you take a piece of

silicon for every electron that was

released from a bond we have leftover

left behind a hole so the number of

holes and the number of electrons number

of free electrons are the same in the in

a pure piece of silicon so we say the

density of holes density of holes is the

same as density of electrons I'll just

say electrons even though we mean free

electrons and it's equal to ni for pure

okay so that's good to know now from now

on we will give you some symbols to

these so that we don't have to write

so the density of holes will be called

lowercase P because P type is positive

charge the density of electrons will be

called n because it's n-type and these

are equal to NI for pure silicon so

that's good to remember we also write P

times n is equal to n R squared Y well

later we will see why we do that but

that's what we need to remember okay all

right so if I give you a piece of

silicon at room temperature you will

have 10 to the 10 free electrons per

cubic centimeter and 10 to the 10 holes

per cubic centimeter that's it right no

more no fewer all right but what if you

want more what if this poor conductivity

is a problem how do we modify the

density of free electrons and holes in

silicon that is the next question that

we need to answer all right so that

brings us to what we called doping so

so we need to answer the following

question how do we modify the density of

charge carriers meaning electrons and

holes in semiconductors for example in

silicon well right now we're stuck with

that 10 to the 10 number because that's

what the equation tells us and we know

that the number of free electrons and

the number of holes are equal in a piece

of pure silicon okay well to get there

we go back to the periodic table and

look at the small section of it to see

if there's any other possibility so let

me draw a small piece of the small

section of the periodic table I will

look at columns that correspond to 4 3

electrons so we know which those are for

example we have silicon here and I think

we have germanium underneath so

germanium we also look at other columns

we have a column with 3 electrons in the

last orbital all with 5 electrons in

that orbital so we have some elements

that fall into this category for example

boron so that's boron which sure has a

symbol of B boron has three electrons in

its outermost shell silicon has 4

germanium has for boron has 3 and then 4

5 we have for example phosphorus US

Morris whose symbol is P no phosphorus

has 5 electrons in its outermost shell

all right so these present interesting

opportunities for us to go and play with

that piece of silicon so far I have said

it I have said it's a pure piece of

silicon but there's no particular reason

why it should be pure what if we go in

that crystal of silicon with all those

and try to introduce some other atoms

maybe boron atoms or phosphorous atoms

what exactly happens something just in

me happened right so let's go ahead and

do that and see what we get so here's

how it goes I'm starting with a piece of

silicon so again we have these silicon

atoms that are bonded together and

sharing their electrons and so on and

then I go and in a very controlled

add for example one phosphorus atom here

and then I again have silicon silicon

etc okay so once in a while I add a

phosphorus atom so what exactly happens

in this case something interesting

happens the phosphorus atom has five

electrons in its outermost shell now

when you start sharing these electrons

with the neighboring silicon atoms it

shares four of them just like the

silicon did before so this phosphorus

atom has one electron that is not K is

able to share with anyone else right

there's nobody else who wants that

electron so there's one electron that

sort of hanging here because it's an

none of these silicon's want it and the

phosphorus has that free electron

available so that electron now can

participate in current conduction that's

a relatively free electron that's

readily available so we don't have to

break an electron out of this bond for

it to conduct current we already have an

electron from this phosphorus atom that

can conduct current so depending on how

many phosphorus atoms are introduced

into the silicon crystal I can have a

larger and larger number of these free

electrons so I can make this overall

device more conductive by having more

and this process of introducing a an

atom of phosphorus or what we call

impurity is called doping so doping

means we take this piece of silicon and

then introduce some non silicon atoms in

here for example phosphorus okay so the

resulting piece of silicon has a new

name this is called extrinsic silicon to

distinguish it from intrinsic or pure

silicon and that we say silicon is doped

or this is an impurity or is extrinsic

silicon and then the phosphorus atom

itself has a name this is called a donor

because it donates an electron to this

current conduction so we have introduced

donor atoms inside this piece of silicon

and now this overall piece of silicon

that has extra electrons for conduction

will have a new name this is what we

call an n-type silicon because it has

electrons more free electrons than pure

silicon and called an n-type silicon or

called extrinsic silicon and so forth

all right okay so this tells us that we

have a situation like this what's

interesting about the situation is that

now we can say that if we introduce lots

of these phosphorus atoms a typical

number is as follows so the density

phosphorus atoms is about 10 to the 15

per cubic centimeters so when we dope

silicon typically we choose a number in

this range depending on what we're

trying to do this is considered lightly

doped this is called heavily doped but

no matter even if you are here and we

see that the number of phosphorous atoms

that we have introduced is much greater

than the number of free electrons or

holes that we had in pure silicon in

pure silicon this was ten to the ten now

we have introduced ten to the fifteen

phosphorus atoms many 10 to the 15 free

electrons coming from the phosphorus

atoms so these electrons coming from

phosphorus completely overwhelm the

electrons that we had already in pure

silicon in other words I can say that

the number of or the density of free

electrons in this doped piece of silicon

and is approximately equal to then

density of phosphorous atoms okay

because we had some already from the

silicon and now we have a lot more from

phosphorus this is so much bigger we'll

just keep it like that and this density

has a name we show that by uppercase n

and then lowercase D n is the density of

the dopants that we're introducing and D

shows that said donor density so we say

that n is approximately equal to n D all

right and it turns out that also we have

n times P is equal to NI squared even

this is no longer pure silicon of course

we saw that for pure silicon before but

even though n has gone up so much and

used to be ten to the ten now it's for

Dean this product is still equal to NI

squared ni that we had before why is

that well because P goes down so much

the number of holes available in this

piece of silicon has gone down why

because these free electrons that came

out of phosphorus atoms very easily went

and filled those holes so the number of

holes much smaller and that's why n

times P is still equal to NI squared all

right so this is what we call an entire

piece of silicon which is dr. to give us

more electrons alright our time is up I