In this video, I want to answer another very pertinent and important question,
is that how does the efficiency of a solar cell behave as a function of temperature?
If I increase the temperature of the solar cell, does my efficiency go up?
Does it, decrease, or it's, not affected at all?
So let me, you know, so the, I'll do the
same way as I did, previously when I analyzed the effect
of, of concentration of light.
I'll see how my short circuit current is behaving as as function of
temperature, and how my open circuit voltage
is behaving as a function of temperature.
So let's first think about the short circuit current.
So short circuit current essentially depends upon the number
of carriers which are collected above the bandgap.
So this short
circuit current would be primarily influenced by how
my bandgap changes as a function of temperature.
So, typically, the bandgap is given as a function of temperature by this formula,
where, when you increase the temperature, when you increase the temperature,
the band gap typically reduces in value. So if the band gap
reduces in, as you increase the temperature, you will absorb, you
know you will essentially absorb a lot more of your solar spectrum,
because, more photons will now be above the bandgap, the new
bandgap which is a reduced bandgap of your solar cell.
So your short circuit current will
essentially increase as you increase the temperature.
This bandgap by
the way, it has a weak dependence on temperature.
Accordingly, the short circuit current has a weak temperature dependence.
It approximately increases by approximately 0.065% for each
each degree centigrade increase in the temperature.
So what I can expect is that if I increase my temperature,
let's say
this red curve is for temperature equal to 25 degrees centigrade,
and then when I increase the temperature by ten degrees centigrade,
so my, my Jsc will accordingly increase by a very small amount, approximately 0.65%.
So I'll draw this Jsc as this white
line which would be closely following but slightly higher
than my red line.
So now the second thing that I turn my attention to is
how does this open circuit voltage behave as a function of temperature.
And I derived this formula for for this open
circuit voltage where it depends upon the short circuit current.
And this J0.
So if I take just a cursory look at this relationship, I might be
inclined to think that this open
circuit voltage also increases as temperature because this is
a temperature term multiplying the whole relationship over here.
And then there's this Jsc term which I with, at which we
had just discussed is also slightly increasing as a function of temperature.
But in fact that is not true.
And the reason is that this, J0 term over here,
it depends
on the square of the intrinsic carrier density.
So this J0 term, it depends upon the square of the intrinsic carrier density.
And, intrinsic carrier density, in turn, depends upon a variety of things, so,
it usually depends upon the the density of state electron
and hole effective masses. And it also
depends upon the band gap of the cell, and usually the relationship
which defines this is, what am writing down over here.
So, it depends upon the temperature using
these you know, pretty complex relationship over here.
So, there's a temperature dependence coming on
from this term over here, which is
coming from the density of the states.
And then there's a temperature dependence coming
on this term over, over here as well.
So my J0, which is proportional to ni squared,
I usually express a temperature dependence of that using this term,
where I'll express this temperature dependence as as a power
function of x, and this power function of x would be,
ideally be 3.
But there could be other terms which
have a temperature dependence over here as well.
So I just write as a, a power dependence of x over here.
And then it depends exponentially on on the band gap using this relationship,
coming from a square of this term. So I can clearly see over here that my J0
will increase you know, increase substantially if I increase
the temperature because I have this power dependence coming from this term.
So if I increase the temperature, this term is causing the J0 to go up.
Similarly I have a power dep, I have exponential dependence coming from here.
So if I increase the temperature, this exponential
dependence on, which is a negative, will decrease.
And both of these
terms will drive this J0 up as I increase my temperature.
So as a result of that, my Voc which you know, has this
J0 in over here. This comes out that this Voc,
it has this particular temperature dependence.
If I plug in this value of of J0
into that relationship, I get a temperature dependence of open circuit
voltage as this, where it decreases as a function of temperature.
And approximately there is, for silicon solar cells, this Voc decreases by
approximately 2.3 millivolt for every degree increase in the temperature,
and this translates to approximately a reduction of 0.36% in my in my Voc
for every degree increase in the temperature.
So now if I think about my efficiency, and, you know, I can think of this in
terms of my fill factor, and Jsc and Voc.
So my Voc
is decreasing is decreasing 0.36% for every percentage over, for
every degree increase in the temperature and my Jsc is not you
know, not rising as fast as the Voc is degrading and
this fill factor also in fact degrades as I increase my temperature.
So overall my efficiency it goes down if I,
if I, increase my temperature. In fact this efficiency,
for, silicon based, for monocrystalline based
or multicrystalline based, solar cell, It decreases approximately by 0.4
to 0.5% for every, every degree increase in the temperature.
So if I have a 10% or if I have a 10 centigrade increase in the temperature
then my efficiency according to this dependence would decrease by 5%.
My cell or my module would would produce 5% less electricity.
And this temperature dependence of Jsc and Voc that I just discussed,
this is typically very well documented in the
specification sheet for each for each solar module.
So for example this is a specification sheet which was released by
BP Solar, which makes solar modules. So it mentions a variety of things.
It contains a lot of useful information.
It tells you what is the maximum power,
what is voltage at which the maximum power occurs,
what the current, which flows at this maximum power point,
What is the Isc, what is the overall
open circuit voltage in this case of this panel
But it also reports this temperature dependence that we just talked about.
So it shows the temperature coefficient of Isc.
And you can see, this Isc,
it's increasing by this 0.065% for every degree centigrade increase in temperature.
Similarly, this Voc, as we just talked about,
it decreases as you increase the temperature.
And this maximum part which is reflective of our efficiency behaves,
this also reduces by 0.5% for every degree of increase in the temperature.
So and again I'm borrowing some, one more chart
from this specification sheet, and it shows this Jsc,
It shows this Jsc
versus this Voc curve over here.
So you can see as you increase the
temperature this Jsc is increasing slightly because my bandgap
of my semiconductor is reducing so now
it can absorb a larger part of the spectrum.
And, but on the other hand you see that this Voc is decreasing
as a function of temperature, and it is decreasing much faster.
As a result of that, the efficiency
decreases as I increase my temperature of my cell.
And this efficiency decrease is different for different kind of cells.
So for crystalline silicon solar cells, this is approximately a decrease of
0.5% per degree centigrade. For some of the
thin-film
technologies, such as amorphous silicon or cadmium
telluride, they fare much much better.
For example cadmium telluride, it the best
temperature performance, and this efficiency only decreases
by half of that half of that as what happens in the case of silicon.
So this amorphous silicon, it also somewhere comes in between.
So these
manufacturer of these thin film solar cells
often tout
these lower temperature coefficient of of their efficiencies.
And they publicize that, especially when they're selling these cell into markets or
into regions where the temperature, the operating temperature is quite high.