WEBVTT - generated by Videoportal Universität Freiburg

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In this unit we will deal

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with the limits on the efficiency of solar
cells.

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In this context, we will also look at various

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solar cell materials.

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In the last teaching units we got to know all
the essential parameters

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that describe the electrical behavior of a
solar cell.

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In addition to all these parameters, the quality
of a solar cell

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also depends on how well it comes up

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to the maximum possible efficiency.

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Let us first deal with

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what are the physically achievable limits

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for the degree of efficiency.

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As we have already learned, the efficiency
results from the product

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of the fill factor, short circuit current and
open circuit voltage

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divided by the incident radiated power.

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The efficiency is therefore largely

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determined by the open-circuit voltage and
the short-circuit current.

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The limits of these two values

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are important for the limits of efficiency.

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Let's take another step back.

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You remember: The photo effect

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lifts electrons from the valence band to the
conduction band.

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If a photon has less energy than the band gap,

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the energy is not sufficient to lift the electron
into the conduction band.

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The photon transmits through the semiconductor
-

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one could also say that the semiconductor is
invisible to the photon.

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If a photon has more energy than the band gap
of the semiconductor,

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an electron is lifted into the conduction band
-

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but it immediately falls back to the energetically
most favorable

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state in the conduction band and releases the
excess energy as heat.

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Both quantities - open-circuit voltage

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and short-circuit current - depend on the band
gap.

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The larger the band gap,

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the larger the potential barrier between the
conduction and valence bands

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and thus also the voltage that the solar cell
can deliver.

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The open circuit voltage therefore rises almost
linearly with the band gap energy.

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The short circuit current depends on the number
of electrons

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that are raised into the conduction band.

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The solar spectrum contains photons with different
energies.

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Thus, in order for the very low energy photons
to contribute

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to the photoelectric effect, the band gap would
have to be small.

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On the other: the larger

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the band gap, the lower the short-circuit current,

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since fewer photons contribute to the photoelectric
effect.

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The product of the open-circuit voltage

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and the short-circuit current is important
for the efficiency.

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Due to the profile of open circuit voltage
and short circuit current,

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this product is zero for very small and very
large band gaps.

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Somewhere in the middle,

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however, a maximum can be found

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in other words: there is a band gap for which

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the efficiency is maximum.

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Let's try to find that optimum.

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In order to do that, we need to take a closer

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look at how the short-circuit current relates
to the band gap.

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In contrast to the open circuit voltage,

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the dependency is not linear.

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Rather, it is related to the distribution

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of photon energies in sunlight - or in other
words: the light spectrum.

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In the last tutorial you already got to know

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the AM1.5 spectrum, which is shown here again.

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The spectrum is typically plotted versus wavelength.

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Let us repeat briefly:

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The energy of a photon is inversely proportional
to the wavelength.

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Light with a small wavelength has a high energy,

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light with a large wavelength has a low energy.

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We can also express the photon energy needed
for the photoelectric effect

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We can also express the photon energy needed
for the photoelectric effect as a wavelength

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In the case of silicon, the band gap energy
is 1.12 eV.

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This corresponds to a wavelength of 1120 nm.

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At higher wavelengths,

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the photon energy is not sufficient for the
photoelectric effect

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and the photons transmit through the semiconductor.

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At wavelengths lower than the cutoff wavelength,

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as the wavelength decreases,

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a larger and larger fraction of the photon
energy is lost

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as thermalization loss.

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Let's return to the open circuit voltage and
the short circuit current.

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While the open-circuit voltage depends significantly
on the bandgap energy,

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the number of photons below the cutoff wavelength

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is decisive for the short-circuit current.

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For simplicity, let us assume that ALL photons

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below the cutoff wavelength are absorbed and
that

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no losses occur during the transport of the
charge carriers.

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For this case, a maximum possible efficiency

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can be calculated as a function of the cutoff
wavelength.

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For silicon with a cutoff wavelength of 1120
nm

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the theoretical efficiency is 32.9%.

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This is the maximum possible

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efficiency for a silicon solar cell.

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So far,

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we have looked exclusively at silicon as a
semiconductor material.

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But what about semiconductors with other band
gaps?

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With a larger band gap, the photons need more
energy

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to lift electrons into the conduction band.

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In the spectrum this becomes clear

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by the fact that the cutoff wavelength becomes
smaller.

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This decreases the number of photons contributing
to the photoelectric effect.

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However, since more energy is now required
for the photoelectric effect,

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the thermalization losses decrease at the same
time.

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As the band gap becomes smaller,

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a larger and larger portion of the radiation
is transmitted.

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In the extreme case of a very large band gap,

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almost all the energy is lost due to transmission
losses

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and the theoretically possible efficiency is
only a few percent.

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The opposite is the case

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when we consider materials with a small band
gap.

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Since the energy required for the photoelectric
effect

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is now lower, more photons can contribute to
the photoeffect.

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The cutoff wavelength increases

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and transmission losses decrease.

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But at the same time, the thermalization losses

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increase, since many photons

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now have much more energy than needed

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for the photoelectric effect.

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If we now reduce the band gap further,

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the thermalization losses increase more and
more.

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In the extreme case of a very small band gap,

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a large part of the energy is therefore lost
as thermalization loss.

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Somewhere between these two extreme cases of
a very small

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or very large band gap, an optimum can be found.

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The relationship between the maximum possible
efficiency

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and the bandgap was first described by Shockley
and Queisser

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and is known as the Shockley-Queisser limit.

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Here you can see the theoretical

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maximum efficiency that can be achieved

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depending on the bandgap of a solar cell.

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The small waves in the curve

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are caused by the course of the solar spectrum.

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If we were to calculate the theoretical efficiency

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for a different spectrum, the shape of the
curve would change.

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The curve shown here refers to the AM1.5 spectrum.

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You can see that the highest efficiency can
be achieved at bandgaps

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between 1.1 and 1.4 eV.

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Silicon is exactly in this range

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with a bandgap of 1.1 eV.

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In reality, however, this

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theoretical efficiency is not achieved.

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For example, the efficiency record for silicon
solar cells

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is currently 26.7%,

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although 32% would theoretically be possible.

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This is because in our

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consideration of theoretical efficiency we
have assumed that all photons

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are absorbed and contribute to the photocurrent.

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However, in any real solar cell, there are
a number of losses -

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for example, reflection losses, recombination
losses, and so on.

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These losses can be minimized,

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but in practice it is not possible to reach
the theoretical efficiency.

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Besides silicon,

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there are a number of other important materials
for photovoltaics.

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For example, gallium arsenide with a band gap
of 1.42 eV,

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Real GAS solar cells

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have reached efficiencies of even 28-29%.

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Another material is CadmiumTelluride

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with a band gap of 1.45 eV

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and a record efficiency of 22.1%.

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These materials differ from crystalline silicon
in one key aspect:

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they absorb light much more strongly.

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As a result, solar cells made of these materials
can be much thinner.

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Here, a thickness of 1-2 µm is sufficient,

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while silicon solar cells are usually 150-200
µm thick.

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This field is therefore also known

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as thin-film photovoltaics.

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We have now learned that the efficiency

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that can be achieved with solar cells is limited.

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While on the one hand it is very motivating
to get closer

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and closer to this theoretical limit, one can
also ask oneself

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whether there is a possibility to overcome
these limits.

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There are several approaches for this,

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of which I would like to briefly mention the
most obvious one

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here: multiple solar cells: In a multiple solar
cell,

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several solar cells with different band gaps
are stacked on top of each other.

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In this way, a larger part of the spectrum
can be used.

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As an example, a three-layer triple solar cell
is shown here.

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The top cell has the highest band gap.

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It absorbs mainly short wavelength light.

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Longer wavelength light is transmitted and
hits the middle cell.

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This cell has a somewhat smaller band gap -

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it absorbs light in a medium wavelength range
(here symbolized as green,

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but is more a spectral range around 750nm (in
the red/NIR region).

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The lowest cell has the smallest band gap and
absorbs

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in the long wavelength range.

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With such a structure, the efficiency can be
increased significantly.

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For example, the peak value for a triple solar
cell is currently 37.9%.

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However, most multiple solar cells are very
expensive

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and are therefore mainly used for space applications.

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This might, however, change in the future,

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as cheaper large band gap semiconductors, like
perovskite,

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which can be combined with Silicone to a tandem
device, are being developed

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and their problems in terms of long-term stability
are being solved.

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I summarize this teaching unit.

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There is a theoretical efficiency maximum

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that depends on the bandgap of the solar cell
material.

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Furthermore, we have seen that the efficiency
limitation

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can be circumvented by using, for example,
multiple solar cells.

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Thank you for your attention.