In the last video I was talking about this

phenomenon of light induced degradation. And it gives a lot of sleepless nights to

manufacturers of amorphous silicon based solar panels especially

because that's where this light induced degradation is is most you know most

severely experienced. And it can reduce the efficiency of these

panels you know, very significantly, you know, to up

to 30 or 40% in the very first few hours of operating the panel.

So this is of course not a good thing.

You want to avoid this light induced

degradation. And then I was explaining in the last video how this light induced

degradation occurs. And I gave you two of these models. This hydrogen bond switching model and the

other model which involves two of these hydrogen

atoms. To explain, you know explain how, how this

light induced degradation occurs. And we saw that you know, no matter which

model you believe in, in fact you know, no matter it's not a, you know, it's

not universally accepted like which model.

is the one which which is the true representation of this of this site in new

degradation.

In fact, if you go to these thin frame

solar technology conferences, in the RAM session you know, when people are

the researchers have some wine and then. And there's at the evening of the conference there's very heated debate

which takes place you know, debating which of these

two models can is the true representation of this light induced degradation. But nonetheless, no matter which model you

you know, you put your money on both of these models

they're. Result in creation of these dangling bond

states. Now you might have already, you know,

guessed that this creation of these dangling bond states is

not a good thing. So what it does in terms of the solar cell is that I can represent the density

of state in my solar cell. So for these amorphous silicon I can

essentially, you know, I have a conduction band state,

and a conduction band tail, and so this is my conduction band and this is my conduction

band tail.

And similarly are the valence band and the

valence band tail. So this would be my valence band and this

would be my valence band tail. And this is my band gap, which for amorphous silicone is

you know close to one point seven eight

electron volt. So now what these dangling bonds do is

that they creates these states within this forbidden region,so within

this region between your valence band and conduction

band.

They create these states which lie right

in the middle of your band gap, so they would be

representing that in a different colour, that means

blue. So they're creating the resulting creation

these dangling bond states. And, they, they lie right in the middle of

these connection degradation and binding states that makes

them a excellent recombination centre. So what happens as a result of result of

these light and degradation. Is that you create a large density or you

increase the density of these dangling bond states, and that

results in a large increased recombination in your

cell. So, so now, essentially, your, your

electron [INAUDIBLE] which are produced.

Instead of getting connected. They can easily recombine. So they can make use of these make use of

these dangling bond states. And they can use it as a recombination center to essentially

recombine with this hole. So this is of course, not a good thing. So you want to avoid this light induced

degradation. And people try a variety of passivation

mechanisms.

So you know, they do different treatments so that these bonds between these silicon and silicon they become

good. Or you know, these bonds are strong enough

so that they're not broken when electron and

hole pair recombine. So one might wonder, you know, why does

this light induced degradation does not happen in this way inside inside

you know a crystalline silicon. The reason is that, for crystal silicon these bonds are essentially, these bonds

between these two silicon atoms they are more

stronger. So when an electron and hole pair

recombine it's not, it's not have sufficient energy to essentially

to essentially break this bond. So that's why this light induced

degradation or this dangling bond creation, is not as prevalent in

let's say crystal silicon.

Nonetheless, this people will have tried

to at least quantify how these dangling bonds are created and

you know, how they evolve over time. So the researchers who work in this field

such as you know, these people who published

this paper, they very meticulously tried to measure

the number of these dangling bonds as a function of the

illumination time. Or the function of the time in which you

keep the cell exposed to sunlight. And it, it clearly shows that as you, you

know as you, as you keep the cell exposed to sunlight, you increase,

you see increase in the number of CR dangling

bonds. And this scale over here, it's plotting

the data in log-log scale. So what this linear, linear slope in the

log-log scale, it means that you have a power law dependent. So you have a power law dependence of this number of dangling bonds on the

elimination time. And then you can measure the slope of this

line and that gives you the exponent. That gives you the coefficient for that

power law. And over here you see that this number of

dangling bonds, it it increases as a, as a function

of time.

With this cube root dependence on the on the illumination

time. Similarly you see over here that, if you

increase your illumination or if increase the

intensity of your light. You see that if you increase the intensity

of the light, the number of these dangling

bond, as you increase the intensity from 50 to 100

to 200, again the number of dangling bond is

increasing. And in fact, if you measure this functional dependence

on this, on this illumination rate or the

generation rate. It again comes out to be this power law

dependence. With the with the dependence of G to the

power of this generation rate to the power of

two by three.

So these things, you know, these things this power law dependence could be very

easily derived by you know, by using these

daunting set of equations. And in fact, you know, there is nothing to

be worried about. There's nothing to be afraid about these

equation. Let me explain the different terms to you. So this you know this first equation, what

it's saying is that, it's it's trying to relate increase the number

of dangling bonds. So what I have to eliminate in respect to

the dangling bonds. So it's saying that, you know, the rate of

increase of the dangling bonds it's essentially

proportional to this forward process. Which creates this timing point that is

you know, this, is proportional to the to the generation rate

of your electron and all.

That of course makes sense. And there's a rewards process which

essentially, the rise in removal of these dangling

bonds. Out of, if you have dangling bonds

present, and you have your hydrogen atom present, this hydrogen can essentially passivate this dangling

bond. So this is a reverse process, and so then

the difference between these two, it gives me the increase in the

number of my dangling bonds. [INAUDIBLE]. Similarly I can write an equation which

delays the increase in the number of my hydrogen

atoms. And it would be again proportional to the

number. It would be essentially equal to the

number of dangling bonds created.

Because every time you create a dangling

bond you create a hydrogen as well. And it would be proportional to the worst

process over here as well. And that is that if you have two of these

hydrogen atoms present, they can essentially you know form a meta

stable state with each other. So that it was process which is

proportional to the square of the concentration of these

hydrogen atoms. So now I have these two differential

equations. So I have the system of differential

equations and I'm you know, how to solve a system of

differential equation. But, you know, to and actually you know, it's

not assuming you know how to solve, a system of

differential equation. In fact, you know, it's a very difficult

set of, if you've forgotten solving differential

equations it might take you a while. So, you know, let me write the final

formula. So, let me write the final expression that

is, you know, if you feel so inclined you can solve these

system of differential equation. But I want to just give you a feel of you know, where this where this power law

dependence come from.

So if you solve this system of equation

you'll get a formula for your number of dangling

bond. And it's related to all these different

coefficients over here. So it's related to this this forward

coefficient. You know, it's related to the generation

rate. It relates to the reverse coefficient. But the two most important things which

stand out is this 2 3rd power dependence on the, on the generation

rate or on the intensity of the light. And, this cube root dependence on the

time. So, of course now, now you have some

understanding of how these dangling bonds are generated and as their, as their

density increases my efficiency falls. So my efficiency if I plot it as a

function of time. So, and let's say at, at t equal to zero,

I at my maximum efficiency. Now as I keep on as I keep this panel exposed to light, the

efficiency will degrade.

In fact, you know, initially I, let's say

I have no dangling bond, so immediately when I start to clear the

dangling bond, efficiency will degrade. But after a while, you know, you already have a lot

of these dangling bonds so addition of these further dangling bonds,

you know, all the damage has already been

created. So the addition of these further dangling

bonds it will there coefficient still keep on reducing, but the rate of this decrease

of the efficiency would be quite low. And we want to measure, you know, at least

when you are by these panels, you should

essentially ask for this efficiency which is measured at this point in time.

And I just call it the stabilized

efficiency. So organizations such as NREL and you

know, other other organizations which new

benchmarking of these cells. So, for example, NREL has this chart which

I'm sure you're all familiar with. Which [UNKNOWN], efficiency of a champion set for different

technology. In looking at this amorphous silicon you

know, let me look at amorphous silicon. Amorphous silicon is the word here. So you can see that for amorphous silicon,

they always mention the term stabilized. So the efficiency level of amorphous

silicon says they've been reported after they've been

exposed to light.

And their efficiency you know, the. It had the degradation efficiency has stabilized and that's where you, you should report the efficiency of these

amorphous silicon. But there are many times you read these you know, these journal or conference

paper and they'll [INAUDIBLE] very high efficiencies for these amorphous

silicon or your, the other thin film technologies. So you should always ask them, you know if

you meet those people, you should ask them that did

you measure those efficiencies the night you made those

solar cells or did you measure it after it was exposed to

sunlight for quite some time. So you should always take those number

with a grain of salt. And you should always look for these

stabilized efficiencies..