In this video, I want to talk about band engineering,
which is needed for making these multi junction solar cells.
Where I grow these different materials with different band gap.
So on top of each other, and then I'll talk about the condition of lattice
matching, which is required when these different
materials are growing on top of each other.
And we'll see that how this requirement of lattice
matching, it dyes my hand.
It restricts me in the mode of band engineering I can do.
So let me you know, start with the example of three junction multi-junction cells.
And these three junction multi-junction cells are you know one of
the highest Efficiency cells that you can buy in the market.
Currently they achieve the efficiency of 43 to 44%,
under a concentration of 500,000 suns. And this efficiency
had been you know, this efficiency of these materials and cell had been a.
you know, it has been continually rising in the recent years.
So if I talk about the three junction cell
I need to find out essentially three different materials.
Let's say this is my material
one, which has the highest band gap, so it will absorb my.
High energy photons, or my blue photons.
So, this is my material which is at the very top, facing the sunlight.
And then I'll have a material which would be below this, which will form my
second junction, and this would absorb, you
know, the intermediate photons, or these green photons.
And below this, I'll have
the third junction, which would be made up of another material.
And this would absorb my, you know, the lowest energy
photons, which are not absorbed by these top two, two junctions.
So, it means that it will absorb these red photons.
Now I can do a simple calculation. You know, I can calculate how much of
the spectrum would be absorbed by this this this this
blue energy material.
And I can calculate it's short circuit current.
Similarly I can calculate the short circuit current for these green and these
red band gap material, and the condition is that these three have to be equal.
And I can apply that boundary condition, and I can, you know, calculate the optimum
band gap, so the optimum band gap of
this blue material, this green material, and this
red material.
Which would give me the highest efficiency.
So in an ideal world if I do that calculation taking the spectrum of the
sun, what I get is this conduit plot and it It is plotted as
a function of a band gap of this material at the top which has the highest band gap.
And then this material in the middle which has the intermediate band gap.
Gap.
And this material at the bottom, which has the lowest band gap.
So, if I do that, then I'm happy to
note that I can achieve efficiency of greater than 50%.
I can achieve efficiency of more than 50%, using this 3 junction cell.
And I've made this assumption that I can, I
can extract each of these absolved photon into electron hoper.
So I've ignored, recombination mechanicims in this analysis.
And then further what I can do is I can
extrapolate this contour into the band gap of these individual materials.
So if I do that, then what I see is that the optimal band gap of the top material
should be should be close to this 0.8 electron volt.
The band gap of this
emitter material should be in between, so if I take this
contour and then extrapolate it to this metal band gap material.
It suggesting that the band gap of this
metal material should be between 1.32, 1.4 electron volts.
And similarly this band gap of the lowest band gap material this bottom material.
If I project
it over here, it is suggesting that this band gap of this
bottom material should be close to, should be close to 0.9 electron volt.
So if I do in fact you know, engineer these different materials such
that I choose the optimum band gap, then I can get efficiencies which are very high.
So now my job now is, is to figure out what combinations are
for semi-conductors which are provided to be by mother nature.
Can provide me these these different band gaps.
At the same time, they can be growing on top of each other.
So the next chart, which I stared at for quite some time, is essentially
this chart which plots the band gap of different semiconductor material.
Different three, five semi conductor material.
Other function of the lattice constant, so as a function of their lattice constant.
And the first thing I'm inclined to look at, the first material I
am inclined to look at is silicon because it's the most abundant semiconductor.
And I make a lot of chips using it.
So I focus my attention on silicon, and then I look
for other materials which have the same lattice constant as silicon.
So actually
then I, you know, when I move my eyes up and down this curve to look
for other materials which have the same bind
gap, which has the same lattice constant as silicon.
Then I'm you know disappointed because there are not that many
three, five materials which have the same lattice constant as silicon.
The only, you know the lone star over here is gallium phosphide which
Has a lattice constant similar to silicon.
So, you know, it's very hard to find three materials with different band gaps, which
can give me this optimum material set for
a three junction solar cell, based on silicon.
I notice that this band gap of gallium phosphide is is larger than what
I need for optimum, so it has a band gap of approximately, 2.2 electron
world which is greater than what I need for my optimal material set.
So I am usually disappointed with silicon. The other material
I turn my attention to next is this close cousin of of
silicon which sits on the right hand side in terms of the lattice
constant, which is germanium. So I look at germanium, and again I
look for other materials which have the same lattice constant as germanium.
So I look up and down this line.
And my light, and you know, and my
eyes popped up because I saw gallium oxide, which
has this band gap of approximately 1.4, which is
the one of the band gaps that I need.
And I can further see there are three,
five materials, which has a lattice constant smaller
than gallium arsenide.
Some of them have lattice constant larger than gallium.
And I can essentially mix these in you
know, mix these two semiconductor three, five semiconductor.
And I can form, let's say, indium gallium phosphide,
with approximately equal mix of gallium phosphide and indium phosphide.
And that has a lattice constant, which is
matched to gallium arsenide, which is matched to germanium.
So,
and it gives me a band gap which is
close to what I need, close to 1.8 electron volt.
So this forms a very good system for
making this making this three junction cell, with
the indium gallium phosphide having a band gap
of 1.8, which is close to the optimum value.
The gallium arsenide which forms the intermediate
cell, and has a band gap of 1.4.
And Germanium which forms my bottom cell and has a band gap of 0.7 ev.
So know that this band gap is you know, is lower than what I needed.
On a, for an optimal cell I wanted a band gap of 0.9 ev but
I'll take what mother nature gives me and I'll form a three junction
cell out of that. So this material system, this germanium
gallium arsenide, and indium gallium phosphide material system is one of the
most you know, most commonly used three junction solar cells.
And, if you do end up making three junction solar cells out of it, you
can see over here, it's my indium gallium phosphide, it's absorbing my high-energy
photons, or my blue photons over here.
Then I have my gallium arsenide, or in this
case gallium arsenide with a very small percentage of indium.
And it absorbing my green light and then I have my germanium, which
has a band gap of 0.7 ev, and it absorbing the rest of this spectrum.
So I immediately see the problem of
you know.
Choosing this germanium which had lower bind gap as compared to the optimum.
So as a result of that since it has a lower bind gap, it is absorbing much
more number of photons as compared to this top and this intermediate cell.
As a result of that the short circuit current, the short
circuit current for the subordum cell which is made of germanium.
Is 25, and the short circuit current of this
top cell is 14 and this middle cell is 14.
So since this germanium has lower band gap, it gives you
this higher short circuit current, but that's not of great use
because my cell is going to be limited by, the aura
short-circuit current is going to be limited by these, top cells.
At the same time, since it has, a lower
band gap, it also gives me a
lower open-circuit voltage, because open-circuit voltage is
directly proportional to the band gap, of
the material from which I'm forming the junction.
So and so it gives me an open circuit voltage of only point two five at one sun.
And germanium also has other loss mechanisms associated with it.
So this germanium, since its band
gap is lower.
It gives me a higher current, which I cannot really use.
And it gives me low open circuit voltage limit
we're on the open circuit voltage of my cell.
The next video we will see some of the
ways we can we can get around this problem.