WEBVTT - generated by Videoportal Universität Freiburg

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Welcome to the PV online course, in this chapter,

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we cover the topic of how a solar cell works.

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In this teaching unit, the photoelectric effect

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will be explained.

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We consider a photon which has exactly the
energy

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corresponding to the band gap of a semiconductor.

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This photon can also be understood as a wave,
i.e.

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as electromagnetic radiation.

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This wave now hits the semiconductor shown.

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There the radiation is absorbed.

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As a result, an electron is lifted from the
valence band into the conduction band.

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A hole remains.

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An electron-hole pair is formed.

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Now, when

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electromagnetic radiation with a photon energy
smaller than the bandgap hits

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the semiconductor, NO absorption

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of the radiation takes place.

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The process of lifting an electron to the center
of the bandgap

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does not occur because there are no allowed
states here.

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This process is shown here only for didactic
reasons,

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it does not exist in reality.

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So the photon does not give its energy to the
electron.

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The electromagnetic radiation has NO interaction
with the semiconductor,

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the light is transmitted.

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If the

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energy of the photon is now greater than the
band gap,

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the previously described process of absorption
takes place.

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An electeon-hole pair is formed.

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However, the electron now has an energy

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greater than the lower edge of the valence
band.

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The excess energy is released

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as heat to the crystal lattice.

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This continues until the electron is

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in the most favorable energetic state possible
in the conduction

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band.

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Which of the three processes described

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takes place depends crucially on the energy
of the photon. This can be calculated with
the help of f_photon: frequency of the photon.

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H is the Planck's quantum of action.

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The energy of the photon can also be calculated

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with the help of its wavelength LAMBDA photon.

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C is the speed of light.

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

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So the energy of a photon is inversely proportional
to its wavelength.

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The wavelength at which the photon

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has exactly the energy of the bandgap E_g is
called the cutoff wavelength.

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Only photons with a wavelength smaller than
the cutoff wavelength

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can lift an electron from the valence band
to the conduction band.

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The figure shows the power density of the solar
spectrum

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in W per m² and micrometer as a function of
wavelength in nm.

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Lambda g, the cut-off wavelength of crystalline

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silicone, with 1120nm

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has now been entered into this graph.

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The part of the solar spectrum

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that can be used for this material is drawn
in orange.

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This is the portion of the spectrum

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with a wavelength less than the cutoff wavelength.

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In a solar cell made of crystalline silicon,

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photons with a wavelength larger than the cutoff
wavelength

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then contribute to the transmission losses.

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In this diagram, to the right side of the cutoff
wavelength.

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This was the 2nd process mentioned earlier,

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with photons having an energy smaller than
the bandgap.

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In contrast, photons, with a wavelength,

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smaller than cutoff wavelength, contribute
to the thermalization

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losses with increasing wavelength.

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This process was described as the third one,
previously.

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Here, the excess energy is released as heat

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to the crystal lattice.

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If we now substitute the values

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and units for Planck's quantum of action, the
speed of light

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and electrone-charge into the formula for the
cutoff wavelength,

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we get the following expression: The cutoff
wavelength

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is 1.24µm times eV divided by the band gap.

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With this formula, you can calculate the cutoff
wavelength very easily.

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Finally, we also consider the annihilation
i.e.

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the recombination of free charge carriers.

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An electron is in the conduction-band, as shown
here.

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In spatial proximity there is a hole (in the
valence band).

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It can now happen that the electron gives up
its energy

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again and falls from the conduction band to
the free place in the valence band.

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It is said: it recombines with the hole that
is there.

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The energy that the electron loses in the recombination
is given off

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in the form of heat or radiation.

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This process becomes

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much more likely if there is an impurity, e.g.

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an iron atom, in the middle of the band gap.

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This additional energy level in the forbidden
zone of silicone

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makes the process of recombination much more
likely.

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The average time that elapses between the generation

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and recombination of a minority charge carrier
is called the lifetime Tao.

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It is about 100µs in doped silicone nowadays.

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We have now learned about the following formation

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phenomena of charge carriers: Electron-hole
pairs

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are formed in an intrinsic semiconductor by
thermal excitation.

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By doping an intrinsic semiconductor,

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foreign atoms (here boron) are introduced

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into the semiconductor (here silicon).

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For further illustration, we only look at the
additionally introduced

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holes, the number of which roughly

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corresponds to the number of doping atoms.

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We can already estimate the order of magnitude

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of the charge carrier concentration: For the
majorities

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it corresponds to the density of dopant atoms.

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The density of the thermally generated charge
carriers

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is then obtained using the intrinsic

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charge carrier density.

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More electron-hole pairs

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are now generated by incident photons.

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On the following slides we will calculate the
concentration

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of these photogenerated charge carriers.

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To do this, we first make a few assumptions:

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The power density of the incident radiation
on the semiconductor is 1000 W/m².

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The sunlight has a maximum intensity

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at a wavelength of 550 nm,

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so we will only look at this wavelength at
first.

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The thickness of the semiconductor

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is 185 µm,

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which is a typical value for a solar cell.

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Another important parameter

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is the lifetime of the minority charge carriers.

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In p-doped silicone, where most photons are
absorbed in a classical solar cell,

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electrons (which are minorities there) live
about 100 microseconds.

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Now, to find out how the concentration of the
holes

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and the electrons in the valence and conduction
band changes

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due to the internal photoelectric effect,

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we must first calculate what the energy of
a photon is.

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To do this, we again use the formula that links
the photon

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energy to the corresponding wavelength of light.

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Here we insert h, c and the light wavelength

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at which the solar spectrum has its radiation
maximum (550nm).

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For the average energy of a photon

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we get a value of 3,6 * 10 ^ -19 joule.

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Next we calculate, how many photons are absorbed
by the solar cell

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To do this we divide the power density of the
incident sunlight

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(1000 W/m²) by the energy of a photon.

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Thus, we get the number of photons that hit

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one m2 of semiconductor per second:

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namely, about 2.8 times 10^21 photons per m2
per second.

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The irradiated photons now create electrone-hole
pairs

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in the crystalline-silicone by the internal
photoelectric effect.

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We assume that only 2/3

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of the photons contribute to the generation

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of charge carriers due to transmission losses.

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Thus, 1.85 times 10 to the power of 21

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electrone-hole pairs are created per m² and
s.

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Now we also consider

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the limited lifetime of the minorities.

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This is 100 µs.

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Of the electron-hole pairs created in one second,
there are never more

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than 1.85 times 10^21 to be found on a m²
at the same time.

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To arrive

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at a charge carrier density per volume,

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we consider the thickness of the solar cell.

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This is here 185 micrometers.

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The generated charge carrier density

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is thus calculated as 10^15 per cm3.

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In p-siicone, the holes are the majorities.

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Their concentration is typically 10^16 per
cm3.

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The concentration of holes produced by light
incidence

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is 10^15 per cm^3 as just calculated.

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The electrons are the minorities in the p-silicon.

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Since holes times electron density always gives
the intrinsic

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carrier concentration squared, we can also
calculate the electron - concentration.

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In the p-region, n_i is 1.1*10^10 cm^3 at 300K
in crystalline silicone

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this then gives a minority carrier concentration.

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in the p-region of 10,000 per cm3.

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The concentration of

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electrons generated by light incidence

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is 10^15 per cm³ as above.

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We now compare the charge carrier densities
of an illuminated semiconductor

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with an unlit semiconductor.

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In the dark, the hole density in the p-region

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is 10^16 per cm3.

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Irradiation with sunlight adds 10^15 per cm³.

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But these can be neglected.

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The electron density in p-doped semiconductors
in the dark

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is 10^4 per cm2.

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Irradiation adds 10^15 electrons,

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which is 100 billion times more.

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The 10,000 electrons present in the doped

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semiconductors can be neglected.

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The charge carrier produced

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by the photoelectric effect have a significant
influence

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on the minority charge carriers.

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The influence on the majority charge carriers,
on the other hand, can be neglected.

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This can be illustrated by a comparison

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with princes and princesses.

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There are 1 million times

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more princes than princesses.

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The princes are the majorities,

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the princesses are the minorities.

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This is of course a very bad ratio!

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If now 1000 princes are added.

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There are still 1 million times more princes
than princesses.

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So the ratio does not change much.

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If, on the other hand, 1000 princesses are
added,

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then the ratio is 1 to 1,000.

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Which, of course, is already much better.

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Let us summarize:

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Photons whose energy is higher than the band
gap

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can lift an electron from the valence band
to the conduction band.

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The wavelength associated with the band gap
is called the cutoff wavelength.

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Electrons can fall back from the conduction
band

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into the valence band and recombine with a
hole.

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In an illuminated doped semiconductor,

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the number of minority carriers is significantly
increased

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while the number of majority carriers remains
about the same.

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We have

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now dealt with the internal photoelectric effect,

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this will later explain the photocurrent in
a solar cell.

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In order to also understand the photo-voltage
in a solar cell,

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we will first look at the charge carrier transport

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and then also the p-n junction in the next
chapters.

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Thank you for your attention.