# Bandgap engineering and lattice matching for multi junction solar cells: part 1 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..