So I spent the last few videos drilling down and detailing this
big tent approach or this big tent definition of solar cell operation.
And it was a very simple definition I said you know
to, for this solar cell to work you just need two things.
And that is you need to have this density of state
bottleneck or in other words you need to have this bandgap, and
the only other requirement was, once you generate these electrons and hole pairs
you should have, you know, one way or another to collect them selectively.
So you should be able to collect these
electrons and holes selectively on these two separate contacts.
And that way you can generate this current.
And we also talk about you know, that this PN
junction, which is how most people think about solar
cells, is one way of achieving, this selective contacts.
But there are other ways such as using this heterostructure or using this
oxide near, oxides with fixed charge near your contacts.
And all of these can be used to you know, engineer selectivity into your contact.
So hopefully, you know, I've beaten this horse to dead, but hopefully
I've made it very clear this big tent definition of solar cells.
And we'll use it, there, you know, again and
again when we talk about these individual solar cell technologies.
So, alright, so, you know, we, we know how the
solar cell would work, but, you know, for this photovoltaic
action to happen,
the first thing we need is, you know, to generate
these sufficient electrons and hole pairs with this incoming light.
So the requirement you know, the next thing I want
to focus is how to trap these incoming photons.
You know, how to convert these incoming photons into this electron and hole pair.
And the broad you know category
which defines this kind of work is generally called as light trapping.
And so you know to give you some
intuition why, why do we need this light
trapping or you know, why do we need
to enhance this trapping of light in my semiconductor.
So let's think of our solar cell as this, you
know, thick slab or this slab of silicon which is you
know, a few, hundred nanometers, few hundred microns in thickness.
So, let's say you now you have this incoming
light with an intensity of, let's say intensity of I.
And it hits this silicon surface.
So right at the top, you know, a
large fraction of it will be just reflected back,
and, so, you know, let's say the reflectivity is defined by the symbol R.
So R times I is my light which is just reflected back, and then, what I get
inside is this transmitted light, and I can define it as, you know, T times I.
And this is what I get into my silicon.
So, right at the, you know, right at the, very beginning, I reflect
a large amount of light back.
And I am not able, I won't be able to,
you know, convert them into these photons into electronic and hole pairs.
But besides that you know, when this light comes and it travels through silicon,
and then you know, it traverses through this you know my few hundreds of
microns of silicon and it reaches this other surface.
And then again, a large fraction of that light is,
is you know, it goes out of this my solar cell.
So, again, let's say this has a transmission probablility
of T1, so, again the transmission probability of T2.
So this is my intensity of light, which is, you
know, just gets out of the system and is not collected.
So, I can capture the physics which is going on between this
reflection and transmission using some simple equations.
So I can, what I need to do is I'll define my refractive index of this incoming medium.
As my N0 and this could be one of the
incoming medium as air but this could be glass as well.
My refractive index of my silicon is essentially Ns.
And then my reflection coefficient, or
my reflectance, which is given by R, just simply defined by this formula, which is
n0 minus ns divided by the sum, and square of that.
And it's essentially you know, it, this formula is what you might remember from
Snell's Law.
And you know to for a full disclosure, this formula is
actually for a normal incidence of light, that is you know right
which is coming at an angle of 90 degrees to this, to this silicon substrate.
And then my transmission, I can define
that as essentially 1 minus my reflectance.
So these are two governing
formulas, and then you know if I look at that then what should I do?
You know, what can I do, so the thing I want to minimize is minimize this R, so
the scheme that I can use is essentially I can apply this anti-reflective coating.
And you might you know know of this,
this term anti-reflective coating, from our discussion on displays.
Where I said, if you have an LCD
display and you want to minimize the
glare, then you use an anti-reflective, coating.
we also previously, when we talked about lithography, we talked about
that, you know, if you have, if you are patterning a resist.
Many times you will avoid the reflection, of light coming up from this bottom layer.
So you put anti reflection coating over here,
so that it doesn't create standing wave, within this
[UNKNOWN].
So it's a similar idea, so what I can do is let me divide my,
my substrate into two parts. So you know, this is a part where I get
this reflectance, what I can put, do is apply this anti-reflection
coating over here. And you know I can select it such that it
has a refractive index of n1 and
my incoming medium again has a refractive index of
n0. And of n0 and then the thing I want to
minimize is this my reflectance back from my from my surface.
So this is the thing I want to, minimize, and another way to
look at it is essentially I want to maximize this transmission of light from
here into my substrate.
So this is transmission probability T1 and this is transmission of coefficient of T2.
So what I want to maximize either I can
say that you know, I want to minimize this R.
And the other way I can look at this is, I want to maximize this T1 and T2 product.
Because I essentially want to maximize the light which comes
into my silicon without getting reflected.
So you know, one can plug these, formulas in, so I can essentially you know,
for each of these layers I can write down this equation of T and
plug this formula in there. And then, what I, when I try to maximize
this, what I get is essentially a refractive index of this medium.
So for this T1, T2 to be max, the value that I get for
my n1 is essentially a geometric mean of my refractive index of my incoming medium
and the refractive index of my semiconductor.
And turn out, you know this formula was derived back
in the early 90s by our good friend Lord Rayleigh.
You might remember Lord Rayleigh from our discourse on lithography,
where he derived another important equation that
of, you know, of our minimum pitch you
can pattern was given by this formula which was also derived by Mr Lord Rayleigh.
But Mr Lord Rayleigh was a very prolific genius, he also derived this formula.
And this is, what is you
know, it's used to determine the optimum refractive
index for anti reflection coef... for anti-reflective coating.
So, if I put this, if I plug these numbers for silicon,
so, silicon has a refractive index of 3.4.
So, you know, if I put that refractive
index of 3.4, and assuming light is coming from.
You know if I put that and
take a square root of I call my friend calculator and calculate this square root.
That comes out to be 1.85, so this number is 1.85.
And this, in fact, is very close to the refractive index
of silicon nitride, which has a reflective index of approximately 1.9.
So you, just by the virtue of this math we derived that
our optimum material to make this anti-reflective coating,
so silicon nitirde would be a good choice.
Another way to look at this anti-reflection coating is
to look and understand it in terms of interference of light.
So what you are trying to achieve by this anti-reflection coating
is you know we are getting one reflectance from this surface.
And,
we are getting another reflection from this surface.
And if, what we are trying to achieve is achieve a destructive interference between
these two ... between these two reflections,
so that there's no light reflected back.
And again this tends to become more wavelength, uh, wavelength dependent.
So you know this optimum thickness of silicon
nitrate, which would achieve this, would then be,
two times, of, this, thickness. Should be equal to lambda by 2
so that these two waves are, are, out of phase, or you know to, to be,
to you know, to take into account this refractive index.
It must be this our, our thickness of my silicon nitride is, should
be, you know, my wavelength divided by 4 times the refractive index of
my material.
And then you know people try to, you
can choose this, optimum thickness for one particular wavelength.
And typically the wavelength people choose it
for is this wavelength for green light,
because most of your spectral power density is centered around your green
wavelength so people try to pick this number. So that It
causes the destructive interference of green light.
And so this is because of you know, this is because of having this
thick anti-reflective coating, this causes a color
change in the way our substrate looks.
So you know if we look, if we start
with, start making a solar cell, we will start with this,
monocrystalline silicon wafers.
And they look, you know, as you can see they look like this grayish in color.
But when we are done making the solar cells, and if you have seen
this, solar panel which has these solar
cells, they look like this, bluish in color.
So what is causing this color change is this anti-reflective coating.
And, this color change, in fact,
does depend upon how thick this, anti-reflective coating is.
So shown here are these multicrystalline solar cells, and
they are covered with different thicknesses of antireflective coating.
And depending upon how thick you choose your silicon
nitride, you get a different color of your solar cell.
And that is why, you know, our solar cells look blue in color.