How the device works and how you can program and erase the flash memory cell.

So the first thing that I want to do is

to compare the flash memory to a transistor device.

So if you look at the flash memory cell, drawn over here is a,

the cross section of your flash memory cell, and drawn

over here is a cross section of a normal, transistor.

So if you compare, your flash memory cell to your

transistor, it looks, very similar, you know a normal transistor has

a source, and a drain, and a gate electrode similarly,

it has, The source and the drain and a gate electrode.

This one has a gate oxide.

This one also has a gate oxide.

The only different thing or the only extra element in a flash memory

cell is you have this extra gate which is, you know, typically a polysilicon gate.

You have this extra gate which is called the floating gate.

And the reason why it's called floating is because there is no direct access to

this gate if you think about it, you know, there is always

a terminal which connects to your source and drain and your gate.

And you can directly apply a voltage to it but as compared to that this is floating

gate, there's no direct electrical contact available to this floating gate.

Also, it's it's surrounded by this this

oxide, material which is supposed to be insulating

so there is no way there could be a leakage but between

my floating gate and my and my source or my drain or

my control gate. So that's why this, this this electrode is

called the floating the floating electrode or the floating gate.

But besides that these two devices look pretty much the same, so if you

remember from your your basics are device physics, of course, and I want to borrow

an equation from there to explain the

principle of operation of this flash memory device.

So, if you remember, from your basic device

physics course, if you have a MOS capacitor.

And you have some charge which is trapped

inside the mass capacitor.

The threshold dependence is essentially of that

mass capacitor as given by this simple formula.

So your threshold voltage is your as you are essentially

the, these are the normal DOMs and this is the extra DOM which comes because of these

track charts as opposed. There was amount of charge Q which

was trapped inside at a distance Dt away

from my gate. The, the change in the threshold voltage

given by simply this Vt is is dependent on Qt

by proportional to how faraway from there and depending upon the

dielectric constant of this this oxide. And you know I can

re-arranged this answer so that e over

dt is essentially nothing but the capacitance.

This capacitance between the gate and this trap

charge and this threshold voltage is essentially given by,

this normal term, then this Qt divided by

this capacity coupling between my gate and this structure.

So if you if you carry that same analogy over here you can

essentially apply the same reasoning that safely

this floating gate is nothing but a layer to trap this charge.

And depending upon whether I have some charge trapped over here or not.

My threshold voltage

would essentially just be dependent on that trap charge by

this formula where I'll have a shift in my threshold

voltage will depending upon whether I have some charge or

whether or not and this shift would be given by.

Is this delta Vt depending upon this change in the charge

in the floating gate and the divided by this capacitance coupling.

And that is in fact the case, so I'm borrowing this from a paper and

it it shows that essentially if you have At.

No charge in your trapped in your floating gate

so this would be the floating gate over here.

And if you have no charge trapped in your floating gate, your electrons

can very easily flow from here to here and so you get,

you get essentially If you have no charge stood, you, when you apply

drain, you apply a gate voltage your device turns on early and.

So suppose you are reading at a particular voltage of VR, you get a high current.

Add that voltage.

And then what happens is if you apply a,

if you have charge stored in your floating gate.

If your floating gate is now.

Is full of electron.

It hinders this channel from turning on and it,

it prevents these, electron, from flowing from here to here.

Unless you apply a high gate voltage which,

overcomes the effect of, this, floating gate charge.

But the drift in the threshold voltage, the delta VT, is

essentially given by the amount of charge that you have in this

floating gate, divided by this capacities coupling between my floating

gate and, my top gate, which is also known as a control gate.

So, this, is essentially, so, as you can see over here, if you have a charge

trapped over here and you apply.

read voltage this you won't get any current so the threshold

voltage has shifted to higher value and you won't be able to

read any current at that particular voltage and you can say

that you know the, the, the device is in a high VT.

Hence the threshold voltage of my transistor

is affected by the amount of charge stored

in this floating gate, by this simple governing equation.

So to understand how the program, in it's behavior of this floating gate device.

It's very important to understand two things.

One is the capacitive coupling And the other one is the tunneling phenomena.

So let's start by first with the,

understanding the capacity of a coupling.

So I can relate the amount of charge into this

floating gate by these, To these different other terminals that have my

source electrode, my drain electrode, my gate electrode, by simply

writing Q equal to cv or simply writing down the maximal equation.

So what I can write down is my charge in

the floating gate, is essentially is related to these different

And my drain is at a potential of VD.

My, channel or my body, is also, also at a potential of zero.

And my gate electrode, my control gate electrode has a potential of, VG.

So what I can do is write down this Q equal to CV formula.

And this Q in my floating gate is essentially related to this, gate volt-,

gate voltages by this, capacitive coupling.

Between my control gate and my floating gate.

It's, related to my source potential by this, Cs capacitance.

It's related to my body potential by this, by this, body of our channel capacitance.

It's also related to this, Drain voltage

by placing capacitive coupling voltage between the gate.

And then I can rearrange this such that I collect

all the terms of which have the floating gate potential and

I collect all the term which have my gate potential

and I collect all the term which have my drain potential.

So if I do that so if I do that then essentially I can rewrite this equation

and this Q in my floating gate as related

to this voltage in the floating gate by these

so here are this capacitance add up and I can call the different

total of these capicitances I can label this as Ct.

So let me simply this further and I want to, what

I want to do is I want to rearrange this equation again

so that I can relate this potential on my floating gate

to the charge on the floating gate and these voltage on

the control gate and the drain voltage.

So what I do is I take all of these terms

on the other side and I can rearrange it such that my

floating gate potential is now related to my the potential I apply on the

control gate and its related by this proportionality factor.

Which is the ratio of the capacitiance coupling with

my control-gate, divided by this total capacitance,

and it's also related to my my

drain voltage potential by this capacitance with

the drain divided by the total capacitance.

And it's related to the charge on the floating gate by this charge on the

floating gate divided by this total capacitance so

this again is a very, very important formula.

Now, let me put it in a box.

And one of the key terms in this formula is this capacitor is the

ratio of this capacitance between my control

gate and my total capacitance is also known as the gate

coupling, ratio. And you want traditionally

want to keep this as high as possible. General rule

of thumb is that you at least, keep it more than 0.60.

A gate coupling ratio of 0.6 means that assuming that, you know, I have

my other terms my drain potential is 0, and my charge to start with is 0.

So those terms vanish. So my floating gate potential is

[INAUDIBLE]

related to my control gate potential by this gate coupling ratio.

And if I will get coupling ratio of point 6, that means

if I apply a ten voltage here it translates to a six

[UNKNOWN].

So if I want a more efficient programming or a faster

programming what you need is a high gate coupling ratio.

So the next thing which is, really important to understand, the operation

of, flash, memory, is this, concept, of, tunneling.

And, tunneling is essentially, you can,

there are three different, regimes, of for tunneling.

One is that when you have essentially no no potential difference

between your between your substrate and your gate.

So shown here is this band diagram which is a

[INAUDIBLE]

capacitor. So you have silicon substrate here, and

you have a gate over here. And when

you have no potential, when you don't have any electric field there's essentially

there's no tunneling current. And then you have two

different regimes. One is at a very high gate potential.

So when you apply a gate potential, which is very high you get

this regime known as fowler norden tunneling, also known as a field emission.

And, in that case your electrons which are tunneling from your

substrate to your gate, they essentially see this barrier for tunneling which is

in the face. in the shape of a triangle.

And do you this barrier?

And they can tunnel through it and its called Farther Northern Tunneling.

The gym in between, that is in between the North tunneling and this

further Northern tunneling is the, is the regime known as the direct tunneling.

So in a direct tunneling your,

your potential is somewhere between 0 volt but not as high as your falling

[INAUDIBLE]

and tunneling voltage.

And in that case your carriers which are tunneling from your, from your substrate

to your gate they see this, again, this potential barrier for tunneling.

But this barrier is now trapezoidal in our case, ten shapes.