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..