So overall my goal is to essentially
minimize this fraction of the total power loss.
So, what I'll do to find out you know, how I can,
how I can do that, is that I'll take a derivative of this.
I'll take a derivative of this with respect to, with respect to the width.
So, I'll get, I'll get, let's See what we get.
So, I'll get a minus wd
by w squared term from this first term over here.
And then I'll get 2 by 3, these
things don't change. w by rsh down over here.
So now this all equated to 0 and you know let me further take this
w square over on this side, so I get w cubed down over here.
And, I'll essentially, you know, if I do that I can take this wd
on the other side as well, of the equation, and I get this relationship.
So, my width which gives me the minimum power loss, or my optimum width, I can
essentially see from here that it would come
out to be the cube of the optimum width.
Is equal to 3 by 2,
this will go to the other side, so this would be v by j
and then I'll get inverse dependent on the sheet resistance.
And then I'll essentially take a cube root on both sides.
So that will give me the optimal weight on the left side, and that
would make, that would give me this
relationship, in terms of my optimal weight.
So there's another w d over here. So this is the optimal
that I should of my cell if I want to minimize my, power loss.
So, I can see that you know, there's not much room to play in most of the terms.
So, you know, the voltage is essentially determined by what kind of cell I'm using.
The current is also determined by the technology.
The dead region, the width
of the dead region is determined by, again technological factors such as how,
how closely you can, you know, align these scribes on top of each other.
So the only, you know, the only hope, or the only lighting,
you know, my shinning star, essentially in this equation is my sheet resistance.
So I will ignore the dependence on
the sheet resistance and this still missing that,
if I'll essentially increase this optimum rate.
What I should do is essentially reduce my sheet resistance.
So again let me show you this in other chart over here,
so this again is plugged the two so two things which
contribute to the power loss. So the first is a dead area, and
that the contribution due to that essentially
reduces as I increase my cell width.
So I'm increasing my cell width.
The contribution to this due to this data is essentially,
which is inversely depending on the weight, it reduces over here.
Then I have the second demo here which is the I squared
R loss, and this is essentially as we discuss it's proportional to the.
Square of
the width of the cell.
So this term, this I square R loss term,
it increases as I essentially increase my cell rate.
So of course I get optimum over here.
And so I get an optimum width, which minimizes this.
minimizes this power loss.
It also kind of depends upon the intensity of light which is incident.
So, if I have less
intense light then I can use the larger, the cell with the larger width.
If I increase the intensity of my light then I will have more currents.
This term, this I squared R term loss will essentially increase.
So, I'll get a.
Slightly less value or a lesser value of this optimal width for my cell.
So then again, you know, looking back at this equation, the shining star in
this equation has to reduce the sheet resistance.
So, you might think you know, okay, you
know, why not just reduce the sheet resistance?
And the first thing that you might think of is essentially increase the thickness.
So, of my TCO material, so if I had this TCO
material, which had a certain thickness, why not double the thickness?
So my sheet resistance of this film decreases.
And that is, that is the you know,
that is something you can think about, but it's not very effective.
And the reason is that if you make this TCO material thicker,
so if you essentially try to increase the thickness of this, TCO material.
It also increases the absorption in this TCO material.
So there'll be a cell which is, which is you know my absorb material.
Such as let's say cattail or amorphous silicon, which is
placed below, below this. Imean all this TCO
material, so, if I'm increasing the thickness
of this TCO material option within this material is going to increase.
And amount of light available radius to this absorb
material which is below this TCO material will decrease.
So,
essentially there's, you know, you can try to
increase this, this thickness of the TCO material.
But if you start to increase the
thickness a lot, the overall power essentially instead
of, instead of improving it, the power loss
starts to increase because you know, you are.
Your cell itself is, is getting less power because more of it
is getting absorbed in the TCO.
At the same time, if you decrease the width of this TCO material, then
you have again more I squared R
loss because your sheet resistance is increasing.
So, there's, there's you know, there's a limited.
Limited play you have available in terms of the thickness of this TCO material.
So now, if I cant, cant do much with the thickness of my TCO material
so what, how do I decrease my sheet resistance?
So, I look at the formula for sheet resistance and it's
given by essence, you know, it's inversely proportional to the mobility.
It's inversely proportional to the doping density.
And it's inversely proportional to the thickness.
So you have seen that you know, we have limited play with the thickness.
But how about these other two terms?
So one thing I can do is essentially you know, increase my.
Now increase my doping density.
And this is in fact, you know, when a readily implied in this thin films.
For example we talked about this zinc oxide and aluminium is added
to it to essentially act as a dopant and increase its doping density.
Similarly in our indium oxide fence.
Ten, for example is to added to 50 increase this doping
density as well.
So that is something which is usually implied to
[UNKNOWN].
But I might caution that you, if you, if you become greedy and start to increase
the doping density a lot, then that doesn't
bode very well on your cell as well.
And the reason is that, you know, if you think about this
[INAUDIBLE]
material.
If you add a lot of these dopins, it creates a very large density of these
carriers inside these, inside the conduction band of this TCO material.
And if you have a very large density of these carriers, these
carriers themselves can absorb light which is called as the free carrier absorption.
And that specially happens in your, in your larger,
longer wavelength light, where they would essentially your absorption coefficient,
if you look over here, it starts to rise if I
add too much doping over here. So, for example this is Aluminium dop I
think oxide and it's contrasted to as undoped I think oxide.
So, for undoped zinc oxide, the absorption coefficient essentially decreases
as the, as the wave length of my light increases.
Just like for you know, for any
normal oxide or any normal semiconductor material.
But if I add a lot of dopense in, into my zinc oxide,
I see that this absorption coefficient starts
to rise, especially for these lower rates.
And the reason for that this free courier absorption.
So again, the point I want to emphasize
is that we should look at are these stones in this sheet
[INAUDIBLE]
equation.
So they're limited plain down to thickness.
We typically add doping but we can't add too much of it.
But, so you see that each of
these parameters, it comes with some limitations.
The only parameter which is unbound and, you know, a lot of focus
now has, in the research community is being, is being devoted to this parameter.
And that is, to increase the mobility.
So, if I can increase
the mobility of, of carriers in my zinc oxide or my.
TCO material.
I can essentially live with a lower density.
I can live with a lower thickness, you know.
Both of these will try to reduce the absorption inside my TCO material.
So, mobility is one term that now a days a lot of
the research is focused on improving the mobility in these TCO materials.