Hello folks.
in this video, I want to investigate this question that, how does the efficiency of a solar cell
how does the efficiency of a solar cell, change with the intensity of the light.
For example, if I have a solar cell and
I'm applying light with the intensity of one sun,
what if I increase the intensity of light to that to be of 10 suns or 100 suns?
What would that do to the efficiency of this solar cell?
So let me start with the basics over here. So i know that my J-V relationship for
my solar cell can be expressed as this, and I can express the condition
of open circuit voltage by equating the total current equal to 0.
So at open circuit condition, my J or my current density in the cell is equal to 0.
So I can plug
for V applied to be Voc and I'll plug the total current to be 0.
So, I'll have have this, condition at, open circuit, voltage
and, basically I can then express my open circuit voltage in terms of this short
circuit current and other parameters. and then I get a formula for, for
open circuit voltage to be equal to equal to kT
by q, natural log of Jsc plus
J0 divided by Jsc. Divided by J0, sorry.
So this Jsc this short circuit current, is more typically much larger than J0.
So i can simplify
this and write it that, approximately equal to kT by
q natural log of Jsc divided by J0.
So now what would happen when I increase the concentration of my light?
So let me think, consider the case, where I increase the concentration and make it 2x.
So if increase
the concentration by 2x, I can expect that
my short circuit current will become 2x as well.
So my short circuit current will become 2 Jc as well.
But what would happen to the open circuit voltage?
So that is a interesting relationship which
is, emerges from this formula that I derived.
So what I see is that, if I increase
my open circuit, if I increase my short circuit current, if I
increase my short circuit current and make it twice, so I make it twice,
so what I see is that my open circuit board will also increase, but not linearly
but much slowly with the logarithmic dependence on the short circuit current.
So what I see is not only is my short circuit current
improving,
but there's also an increase in the open circuit voltage,
which comes from this from this JV relationship.
So what I see is that instead of having Voc, I'll see a Voc
plus delta as my, plus delta, as my open circuit voltage.
So my new IV relationship will essentially look something like this,
where I have a slight increase in my Voc as well.
And I can assume you know, I'll make the approximation that my fill factor remains
the same. So i can write my efficiency as
essentially my Jsc times my Voc,
divided by the incident power. So when I increase my concentration to 2X,
I'll get essentially twice increase in my short circuit current.
I get a twice increase in my incident power.
But I've seen my Voc is also now slightly increased, as given by this relationship.
So I'll get Voc plus this delta increase in the Voc.
So my efficiency, if I compare it as a concentration of 1 sun, versus if I
compare the efficiency, at the concentration of 2 sun,
I see that i see increase in my efficiency.
So what this analysis is suggesting is that my
efficiency increases as I increase the concentration of the light.
But there are some caveats to this.
So what I've assumed in this analysis is that my temperature of the cell did not vary.
Typically, if you have very large current flowing or if you have a larger
intensity of, of, light, which is, incident on your cell,
temperature can increase. And, that
decrease in efficiency that will be a subject of another video, but if the
temperature rises, then this efficiency increase might
not hold true.
Similarly, when I increase my concentration I get
a proportional increase in the current, so if I
increase my concentration from 1x to 2x I'll
get you know, corresponding 2 times or x time
increase in my in my current.
And my resistive losses in my circuit are, as
you know, proportional to the square of the current.
So if I have a large resistance such
as serial resistance, or some other resistance is
present in my circuit, that would essentially also
increase these that would lead to increasing these losses.
And that can decrease my overall efficiency of the light.
So typically
due to these considerations, the concentration
of light, the maximum concentration of light
that is used is, is limited to around 500x, or at maximum, around 1000x.
And the most highest efficiencies of multijunction or III-V based solar cells,
they use, they make use of this fact that your efficiency increases
as you increases your concentration, and they use these very high
concentrations to boost up the efficiencies in these solar sets.