Download How does a solar cell work? by Finley R. Shapiro First, let`s be clear

How does a solar cell work?
by
Finley R. Shapiro
First, let’s be clear that you don’t need to know how a solar cell works internally to design a perfectly good PV
system. You never deal with the internal workings, and most PV system designers never even need to deal with
individual cells. As long as you understand the external characteristics of solar modules you’ll do fine.
In spite of this, many treatments of PV system design and installation feel the need to touch on the internal
workings of a solar cell. The problem is, these treatments often have mistakes. No one catches them, because
they don’t really matter to what is being taught and learned. And the mistakes propagate, because people
prepare their own explanations based on others they have seen, without recognizing the mistakes.
This treatment will, of necessity, be very limited in scope. It will touch only briefly on, or skip entirely, many
important aspects of solar cells. It will discuss only briefly topics that science and engineering graduate students
spend years trying to grasp fully. Lastly, it will only discuss how a single crystal silicon or polycrystalline silicon
solar cell works. Amorphous silicon thin film solar cells work a little differently, as we mention at the end.
Most of the phenomena we will discuss are the same that govern transistors, integrated circuits, and lightemitting diodes. As such, these discoveries during the 20th century are among the most important advances in
the history of technology.
Hopefully, this treatment will convey some real understanding of what is happening inside the solar cells that we
place in the sunshine.
Let’s start with chemistry. You may notice that the chemistry of silicon is basically the same as the chemistry
you may have once studied for carbon. This is because silicon is directly under carbon in the periodic table, and
both are part of the 4A group of elements. (Pictures of the periodic table are available at many web sites. See,
for example, http://periodic.lanl.gov/default.htm.)
Silicon crystals have the same structure as diamond, which is one of the structures carbon can have. Diamond is
also a semiconductor, and can be used to make electronic devices, although silicon ones are better for most
applications. (The other form of solid carbon, graphite, is not a semiconductor.) The chemistry of silicon is
similar enough to the chemistry of carbon, the basis of life on earth, that science fiction writers have speculated
about silicon-based life elsewhere in the universe. Perhaps they use diamond electronic devices there.
Some groups of elements have commonly used names, such as the alkalis, the halogens, and the noble gases.
Some people even remember the chalcogens and the pnictides. Surprisingly, given the great importance of the
4A elements, their name, “the tathogens,” is almost entirely forgotten.
Each silicon atom has a nucleus with 14 protons. This is what makes it silicon instead of some other type of
atom. Since each proton has a unit of positive charge, the silicon nucleus pulls on electrons until it accumulates
14 negatively charged electrons to make it neutral. If the atom has less than 14 electrons, it will pull on nearby
electrons to try to get more. The attraction between the positive charge of the nucleus and the negative charge
of the electrons holds the electrons near the nucleus, although under some circumstances they can get away. If
a silicon atom has 14 electrons, it has a net charge of zero, and we say that it is “charge neutral,” or just plain
“neutral.”
By the laws of quantum mechanics, confined electrons must be in specific states, called “quantum states,” and
only one electron can be in a quantum state. A silicon atom has 10 electron states relatively close to the
nucleus. A silicon atom’s first 10 electrons go into these states, where they are tightly held and not particularly
important for the rest of our discussion. A neutral silicon atom’s remaining 4 electrons can’t fit into the 10
states close to the nucleus, so they occupy 4 of a set of 8 states farther away from the nucleus. These are the
electrons that can actually do things we are interested in.
(Chemistry note: Groups of quantum states with similar characteristics for electrons around an atom are called
“shells.” Shells are divided into subshells, which are smaller groups of quantum states within a shell. The
quantum states for the first 10 electrons around a silicon atom make up the K and L shells. The last 4 electrons,
which are the ones we are interested in, are in the s and p subshells of the M shell.)
When a silicon atom comes close to another silicon atom, or to one of several other types of atoms, the two
atoms begin to influence one another’s quantum states. At the right distance, a quantum state from each atom
will become two shared states in between the atoms, and an electron from each atom will occupy these two
states. We think of the electrons in these shared quantum states as “glue” that holds the atoms together. It is
called a “chemical bond.”
A silicon atom is able to make chemical bonds with up to four other atoms, and in pure crystalline silicon the
atoms are all bonded together this way. Each silicon atom is bound to four other silicon atoms, each of which is
bound to the first one plus three more, and so forth. You can see a picture of the structure of a silicon crystal at
http://en.wikipedia.org/wiki/Silicon#Crystallization.
With all of these silicon atoms bonded close together, each atom affects not only the quantum states it shares
with its four nearest neighbors, but also the quantum states that are farther away. All of this interaction winds
up creating a large set of nearly identical quantum states called a band. In a silicon crystal with N atoms, there is
a band of quantum states called the “valence band,” which has exactly 4N quantum states. This is just enough
space for the 4N electrons that cannot fit into the atoms’ inner quantum states but are necessary to make the
crystal charge neutral.
But remember we said that each atom had 8 quantum states for its four outer electrons. Four of these states
wind up merging into the valence band. The other 4, along with other unoccupied quantum states, merge into a
different band called the “conduction band.” The valence band has a lower energy, and electrons tend to go to
the lowest energy state available. At absolute zero, in theory, the 4N electrons in a silicon crystal would occupy
the 4N quantum states in the valence band, and all of the quantum states in the conduction band would have no
electrons. We say “in theory” because 1) it is impossible to reach absolute zero, and 2) other weird things start
happening in silicon when the temperature gets close to absolute zero.
Atoms in a crystal vibrate around their position, even though the chemical bonds with neighboring atoms largely
hold them in place. The warmer it is, the more the atoms vibrate, until eventually the crystal breaks apart and
becomes a liquid or a gas. In a silicon crystal, every now and then the atoms vibrate in the right way to hit an
electron in the valence band and “kick” it up into the conduction band.
In some ways, an electron “likes” to be up in the conduction band. The conduction band is almost entirely
empty, and when it is in the conduction band an electron can move around a little in ways it can’t when it is in
the valence band. We call an electron in the conduction band a “free electron,” to distinguish it from the
electrons that are still in the valence band or in other quantum states. A free electron moves around more
easily than other electrons, but it still is not free to leave the crystal.
When the electron went up into the conduction band, it left behind a quantum state in the valence band that is
now empty. The empty quantum state means that there is a net positive charge for the vicinity. Due to
something called the “effective mass theory,” the empty quantum state and its associated positive charge act
like a positively charged particle. We call this positive particle-like thing a “hole.” Even though it is really just an
empty quantum state in the valence band, a hole in the valence band can move around the crystal very much
like a “free” electron in the conduction band. We can even call it a “free” hole. The difference is that a hole has
a positive charge, while a free electron has a negative charge.
Life for the newly free electron and the hole it left behind is not peaches and cream. Negatively charged free
electrons and positively charged holes attract each other, and when an electron and a hole get close enough
(under the right circumstances), the free electron falls into the hole, which is to say the electron goes from the
conduction band back to the valence band. The hole ceases to exist. The free electron also ceases to exist,
becoming a normal electron in the valence band.
We call the mutual annihilation of a hole and a free electron “recombination.” In silicon, an electron that makes
it up into the conduction band rarely recombines with the same hole it left behind, but rather it usually
recombines with some other hole it encounters. Electrons in silicon are like this. In some other materials, it is
more common for a free electron to recombine with the hole it originally left behind. This process is called
“geminate recombination,” because the newly created free electron and hole are thought of as twins.
When silicon is in equilibrium, the rate at which free electrons and holes are generated (that is, the rate at which
electrons are kicked up into the conduction band by vibrating atoms) must equal the rate at which they
recombine, so that the total number of free electrons and holes remains constant. The generation rate is
determined by how much the atoms are vibrating, which is determined by the temperature. The recombination
rate, however, is determined by how quickly free electrons and holes find each other. The more electrons and
holes that are around, the more quickly they find each other and hook up.
So, if n is the concentration of free electrons and p is the concentration of holes, we have
recombination rate = A·n·p = generation rate
where A is (approximately) constant. In a pure silicon crystal, the electron concentration and the hole
concentration are equal, so n=p and
√
We call this concentration of electrons the “intrinsic carrier concentration” and write it ni. The generation rate
increases rapidly with temperature while A is much less affected by temperature, so as a result ni increases
rapidly with temperature.
To make this a little more concrete, here are some values. The atomic density of silicon in a pure crystal is about
5x1022 atoms per cubic centimeter. (In this field, concentrations are commonly given as some number per cubic
centimeter, even though the actual volumes are usually smaller than a cubic centimeter. We will write “per
cubic centimeter as either “/cm3” or as “cm-3.”)
With four outer electrons per atom, we have 2x1023 outer electrons/cm3, and the valence band has space for the
same 2x1023 electrons/cm3. At room temperature ni is about 1010 free electrons/cm3. So there is about 1 free
electron in the conduction band for every 20 trillion electrons in the valence band. This is about the same ratio
as $1 out of the national debt. Not very much. Viewed another way, there is about one free electron and one
hole in a cube about one fiftieth of a millimeter on each side, which is actually a very big volume for what we are
talking about.
The element phosphorus is right next to silicon on the periodic table. A phosphorus atom has a nucleus with 15
protons instead of 14, but its quantum states are very similar. One of the great discoveries of the 20th century is
that if you put very slight amount of phosphorus atoms into silicon, it bonds to the silicon atoms around it just
like a silicon atom does.
However, with a phosphorus atom in a place where a silicon atom would be in a pure silicon crystal, charge
neutrality requires that the crystal have one additional electron. So a silicon crystal with a little phosphorus in it
has 14 electrons for every silicon atom plus 15 for every phosphorus atom. As with silicon, 10 of phosphorus’s
electrons stay very close to the nucleus, and we don’t need to concern ourselves with them. We only need to
consider silicon’s outer 4 electrons and phosphorus’s outer 5.
If NP is the number of phosphorus atoms in the crystal that are acting like silicon atoms, and Ntotal is the number
of silicon and phosphorus atoms, then the total number of outer electrons in the crystal needs to be
4Ntotal + NP
But since the quantum states are pretty much the same with either atom, the valence band can still only hold
4Ntotal electrons. The additional NP electrons have to go in the conduction band, meaning that they are free
electrons! These free electrons don’t even leave holes behind. But instead, they leave positively charged
phosphorus atoms behind. Because each phosphorus atom “donates” an electron to the conduction band,
phosphorus atoms are called “donors” in silicon. Arsenic, which is right under phosphorus in the periodic table,
is also used as a donor in silicon. Since it doesn’t matter that much whether the donors are phosphorus, arsenic,
or a combination, we write the concentration of donors as ND. A concentration of 1017 donor atoms/cm3 in
silicon is considered to be modest doping. This is about one donor atom for every half million silicon atoms.
It is possible for a donor atom to hold on to its last electron rather than donating it to the conduction band. In
this case the electron is in a quantum state that is neither in the conduction band nor the valence band. In
phosphorus-doped crystalline silicon at room temperature this is extremely uncommon. However, it does
happen in other semiconductors, and is more common at lower temperatures. When electrons are with their
donor atoms rather than where you want them in conduction band, it is called “freeze-out.”
One phosphorus atom in every half million silicon atoms is not enough to change the generation and
recombination processes significantly. We still have
recombination rate = A·n·p = generation rate = A·ni2
But now with all of the electrons from the phosphorus atoms in the conduction band, the additional free
electrons that are added to the conduction band by vibrating atoms are insignificant. The concentration of free
electrons is, to a very close approximation, equal to the concentration of phosphorus atoms. We still have
n·p = ni2 ≈ 1020 cm-6
so when n goes up, p goes down. If we have 1017 phosphorus atoms /cm3, giving us n=1017 free electrons/cm3 in
the conduction band, we can have only about 103 holes/cm3 to satisfy the equation above. This is one hole per
cubic millimeter! Basically, due to the phosphorus doping, any time vibrating atoms generate a free electron
and a hole, the hole recombines with some electron so quickly that the steady state concentration of holes
never gets above a very tiny amount.
The amazing, and extremely important, thing here is that by adding one phosphorus atom for every half million
silicon atoms (2 parts per million), we’ve increased the concentration of free electrons by a factor of 10 million.
We’ll see soon why this is so important.
It is important to realize that adding phosphorus to silicon does not make the material negatively charged.
(Some people incorrectly think it does.) The crystal still has 14 electrons for every silicon atom and 15 for every
phosphorus atom, and it is charge neutral. The 15th electron from every phosphorus atom winds up in the
conduction band, and moves around rather than staying close to its phosphorus atom. The phosphorus atoms
have only 14 electrons close in, and hence actually have a positive charge. But this is neutralized by some
electron in the general vicinity, so the crystal is overall charge neutral.
Like phosphorus, aluminum atoms (in small quantities) act like silicon atoms when they are in a silicon crystal.
However, an aluminum nucleus only has 13 protons, so a neutral silicon crystal with a little aluminum in it only
has 14 electrons for every silicon atom and 13 for every aluminum atom. So if Ntotal is the total number of silicon
and aluminum atoms, and NAl is the number of aluminum atoms, then the number of outer electrons is
4Ntotal - NAl
But the valence band of the silicon crystal still has space for 4Ntotal electrons. This means there will be NAl empty
spaces in the valence band, or holes. Since holes can float around in the valence band just like free electrons
float around in the conduction band, the holes do not generally stay close in to aluminum atoms. This means
that an aluminum atom will have 14 nearby electrons, and will have a negative charge. It will be neutralized by
a hole in the general vicinity, although generally farther away, and the crystal overall will be charge neutral.
Dopants that increase the number of holes in a crystal are called acceptors, because they accept an electron
beyond what is necessary to be neutral, and thus allow there to be a “free” hole.
Just like arsenic is one below phosphorus in the periodic table, and arsenic acts like a donor in silicon like
phosphorus does, boron, which is one above aluminum in the periodic table, acts as an acceptor in silicon just
like aluminum does. As it turns out, boron works much better as an acceptor than aluminum does, and is almost
always used. It is not important that boron has 8 fewer protons and 8 fewer inner electrons than aluminum
does. It’s the outer electrons that are important to us.
If we put 1017 boron atoms/cm3 in a silicon crystal, the result is 1017 holes/cm3 in the crystal’s valence band.
Since our equation
n·p = ni2 ≈ 1020 cm-6
still holds, we will now have only 103 electrons/cm3 in the conduction band. Adding one boron atom for every
200,000 silicon atoms increases the number of holes by a factor of 10 million, and reduces the number of free
electrons in the conduction band by the same factor. The product of the concentrations of electrons and holes
remains constant.
The small amounts of impurities such as the donors phosphorus and arsenic and the acceptor boron are called
“dopants.” Dopants do not have to be donors or acceptors. Gold is sometimes used as a dopant in silicon even
though it is neither a donor nor an acceptor. It is useful because gold dopants increase the recombination rate.
This is valuable in some specialized types of silicon transistors.
What happens if we have both donor and acceptor dopants spread uniformly in the same crystal? They
counteract each other. In a common situation, we may have 1015 boron atoms/cm3 and 1018 phosphorus
atoms/cm3. Of the extra 1018 outer electrons/cm3 that the phosphorus brings to the crystal, 1015/cm3 will go to
the valence band to make up for the outer electrons that the boron atoms did not bring. The remaining
0.999x1018 extra outer electrons/cm3 become free electrons in the conduction band. If for some reason this
isn’t enough and we really need a full 1018 free electrons/cm3, we could always put in 1.001x1018 phosphorus
atoms/cm3.
Likewise, if we have more boron than phosphorus, some boron atoms will counteract all of the phosphorus
atoms, and the rest will give us holes. Over all, if there are more donors than acceptors, the number of free
electrons is the difference between the number of donors and the number of acceptors. If there are more
acceptors than donors, then the number of holes is the number of acceptors minus the number of donors. (All
of this assumes that the donor and acceptor concentrations are much larger than ni. If not, we need to take ni
into account in calculating the number of free electrons and holes.)
So we’ve seen that with small amounts of phosphorus or boron we can dramatically alter the number of free
electrons and holes. Now why is this important?
Electrical current moves through a uniform silicon crystal as either moving free electrons in the conduction band
or moving holes in the valence band. All of the other electrons in the crystal cannot move, and hence cannot be
part of an electrical current. A parameter called μe (“myu-ee”) describes how fast free electrons in the
conduction band move when a voltage is applied, and μh determines how fast holes move in the valence band.
In silicon, μe is about three times bigger than μh. You might think that this is because electrons are real while
holes really are not. But this is not the reason.
So the ability of a silicon crystal to carry current in response to an applied voltage is proportional to
μen + μhp
Now we see one important reason for putting in dopants. In pure silicon with no dopants, silicon’s ability to
conduct electricity is proportional to
μen + μhp = μeni + μhni = (μe + μh)·1010
This number is not very big. But if we put in 1016 phosphorus/cm3, which is 1 phosphorus atom for every 5
million silicon atoms, the conductivity goes up to
μen + μhp = μe·1016 + μh·104 ≈ μe·1016
This is more than a factor of half a million more than for silicon with no dopants. If instead we put in 1016 boron
atoms/cm3, the conductivity goes up by more than a factor of one hundred thousand. (If we put both in we’re
back where we started.)
If a material has only donors, or more donors than acceptors, we call the material “n-type.” The free electrons
are the dominant charge carrier, and we call them the “majority carrier.” In this material we call holes the
“minority carrier.” Likewise, if a material has only acceptors, or more acceptors than donors, we call it “p-type.”
In this material the holes are the majority carrier and the electrons are the minority carrier.
Now that we’ve covered all of this, there’s only one more phenomenon we need to cover before we’re ready to
talk about solar cells.
If we shine light on a silicon crystal, some of the light is absorbed and “kicks” electrons from the valence band up
into the conduction band. Just like when the atoms kick an electron up, light creates equal numbers of free
electron and holes.
If the light we shine on the crystal is simply a short flash, the concentration of electrons and holes will go up
initially, and then after the flash ends the concentrations will gradually return to their original values. On the
other hand, if we apply a steady amount of light, electron hole pairs will continue to be generated, and the
electron and hole concentrations will increase until they reach a steady-state value at which the recombination
is equal to the new generation rate.
Let’s put some specific numbers into this. We saw that the generation rate due to vibrating atoms is
A·ni2 = A·1020
Suppose we have a silicon crystal with 1015 boron atoms/cm3 and no donors, so p=1015cm-3 and n=105cm-3. We
shine enough steady light on it to increase the generation rate to A·1026, totally overwhelming the generation
rate by vibrating electrons. To a close approximation, the electron concentration goes up to about n=1011cm-3.
The hole concentration, on the other hand, stays at about p=1015, plus about 0.01%. Even though the ability of
free electrons to carry current has gone up by a factor of one million, current conduction is in the crystal is still
dominated by holes, and the entire ability of the crystal to carry current only goes up by about 0.02%. It is a
very slight change. But this is only a simple uniform piece of silicon. In more complicated devices we’ll find that
the minority carrier current is quite important.
Now let’s start manufacturing a solar cell.
We start with molten silicon, and from it we grow a solid column or block of silicon. We include a little boron in
the molten silicon, and it turns out that this actually helps the column or block grow. We adjust everything so
that our final product has a concentration of 1015 acceptors/cm3. We then slice our silicon into wafers.
Next we take these p-type wafers, and expose the top surface of each wafer to phosphorus, using one of several
possible approaches. We allow enough phosphorus to diffuse into the top of the wafer to create a thin top layer
that is n-type with an excess concentration of 1018 donors/cm3 beyond the number of acceptors.
So if we go down into the wafer from the surface, at first the silicon is n-type, but then part way down it
becomes p-type. We adjusted our process parameters so that the n-type region is much thinner than the p-type
region, and also so that the n-type region is much more heavily doped than the p-type region. We call the place
where the silicon goes from being n-type to being p-type the pn junction.
We would like our pn junction to be perfectly abrupt, with 1018 donors/cm3 above it and 1015 acceptors/cm3 and
no donors below it. In practice we can’t make it perfect. There’s also a trade-off between how abrupt we make
it and how expensive our process is, and with solar cells it’s very important to keep costs down. But for our
educational example we’ll assume it’s perfectly abrupt.
Now you might expect with our abrupt pn junction that the free electron concentration on the n-type side
would be 1018 free electrons/cm3 right up to the junction, and then jump abruptly to 105 on the p-type side. But
this isn’t quite what happens.
Imagine you have a box with two equal sized compartments separated by a barrier. In one compartment you
put a concentration of 1018 atoms of gas, and in the other you put only 1015 atoms of the same gas. Then you
remove the barrier separating the two compartments. The gas quickly mixes due to the random motions of all
of the gas atoms. This process is called “diffusion.” Pretty soon you have the same concentration of gas
throughout the box.
Electrons in a conduction band also diffuse much like gas particles, with one BIG difference. Electrons are
charged. When electrons on the n-type side of a pn junction start diffusing over to the p-type side, they leave
behind a bunch of positively charged donor atoms.
Remember how we found that in a phosphorus-doped silicon crystal, one electron for every phosphorus atom
floats around in the conduction band, leaving behind phosphorus atoms with a positive charge. Now, when
these electrons in the conduction band diffuse over to the p-type side of a pn junction, the positively charged
phosphorus atoms can’t go with them. The phosphorus atoms are stuck, held in place by the surrounding silicon
atoms. But because the phosphorus atoms are positively charged and the electrons are negatively charged, the
phosphorus atoms exert a pull on the electrons that diffused over to the other side.
A balance develops between the desire of electrons to diffuse over into the p-type side, and the pull of the
positive charges that tries to bring them back. This balance follows an equation first developed by Albert
Einstein as a follow-up to the work in his Ph.D. thesis. (Yes, even he had to write one.) Einstein was actually
investigating particles, not electrons (conduction bands hadn’t been discovered yet, and the electron itself had
only been discovered a few years before), but it is the same equation and is known as the Einstein Relation.
Einstein published this work in 1905, the same year he published his first two papers on the Special Theory of
Relativity and his paper on the Photoelectric Effect. While Einstein is most famous for the other three, the paper
on diffusion was the only one that was quickly accepted by the scientific community.
What we have at a pn junction is really a semi-permeable membrane. One type of charge is able to cross the
barrier and the other is not, but the immobile charges exert an attractive force on the charged particles that do
cross. In our case the negatively charged electrons can cross the pn junction; the positively charged phosphorus
atoms cannot, but exert a pull on the electrons. The same thing happens in our nerve cells. The equations are
even the same, although people generally use different units and symbols. In our nerve cells, one type of
charged atom is able to cross between the inside and outside of the cell, while the other is not. Charges build up
on opposite sides of the cell’s surface. Then, when your brain wants to send a signal to another part of your
body, it opens pores in the membrane to allow the other type of charge to pass through, neutralizing the charge
that had crossed. This neutralization propagates down your nerve all the way to your toes, and is recognized by
your toe muscles to make your toe wiggle. It can even make it from a whale’s head to its tail. So nature
discovered all of this long before the first pn junction.
But back to our pn junction, if the phosphorus atoms do move across it destroys the junction. This is one
possible thing that can happen when a junction “burns out,” after which it is generally thrown out. (By contrast,
after the two sides of a nerve cell membrane neutralize, the cell re-establishes its “junction” and space charge
layers in a fraction of a second. Nature is always fascinating.)
The result of the balance between the tendency of free electrons to diffuse across the junction and the force to
pull them back is a concentration of electrons that changes smoothly near our pn junction. Far away from the
junction on the n-type side, the concentration is 1018cm-3. Then close to the junction, but still on the n-type side,
the concentration of free electrons decreases because some have crossed over to the other side. The
concentration of electrons continues to decrease as we get closer to and then cross the junction. Eventually, as
we get well into the p-type side, the concentration reaches 105cm-3 and stays there for the rest of the p-type
side.
Holes in the valence band act just like electrons, except that the holes are positively charged. Some of the holes
near the junction on the p-type side diffuse across the junction, but are limited by the fact that they are pulled
back by the negatively charged boron atoms they left behind.
We can calculate the actual concentrations of electrons and holes at different distances from the junction by
solving some complicated equations to get a complicated formula. But instead we’ll make a simple
approximation that actually is reasonably close.
We’ll assume that on the n-type side, within a certain distance from the junction all of the free electrons have
diffused over to the p-type side. Since there are no free electrons in this region (in our approximation), we call it
the “depletion region.” Beyond the depletion region, we assume there are 1018 free electrons/cm3 as
determined by the doping level, and the material there is charge neutral. Inside the depletion region, we still
have 1018 positively charged phosphorus atoms/cm3. So this depletion region has a positive charge, and we also
call it the “space charge region.”
Over on the p-type side of the junction, there is also a depletion region where the holes have diffused across to
the n-type side. In this region there are (approximately) no holes, but there are negatively charged boron
atoms, making this another space charge region. Beyond the depletion region, the hole concentration is
(approximately) 1015cm-3 and the electron concentration is about 105cm-3.
So, somewhat counter-intuitively, right near the junction we have a positively charged region on the n-type side,
and a negatively charged region on the p-type side. These charges try to pull free electrons in the direction of
the n-type side and holes in the direction of the p-type side, but are counterbalanced by the desire of the
electrons and holes to diffuse from areas of high concentration to areas of low concentration. However, even
though there are positive and negative space charge regions, and positive and negative charge carriers
(electrons and holes), the charges all cancel out and the device as a whole is charge neutral. (If it weren’t, it
would grab electrons from, or give off electrons to, anything it touches to become neutral.)
Top electrical contact
Entry area for light
n side
+++++++++++++++++++++++++++++++++++++++++++
- - - - - - - - - - - - - - - - - - - - - - - - - - p side - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Back electrical contact
n side except very close to junction:
More donors than acceptors
Many free electrons and very few holes
Charge neutral
n side very close to junction:
More donors than acceptors
Very few free electrons or holes
Positively charged “space charge region”
p side very close to junction:
More acceptors than donors
Very few free electrons or holes
Negatively charged “space charge region”
p side except very close to junction:
More acceptors than donors
Many holes and very few free electrons
Negatively charged “space charge region”
Figure 1. Regions of a typical solar cell. This figure is not to scale. The positive and negative space charge regions have
equal but opposite charges, so the entire device is charge neutral. In the device described in the text, the concentration of
positive charge in the positive space charge region (on the n-type side) is 1000 times greater than the concentration of
negative charge in the negative space charge region (on the p-type side), but the positive space charge region is also 1/1000
the thickness of the negative space charge region.
Don’t despair. We’re close to the end of our story.
Finally, we’re ready to shine light in from the top of our solar cell. The light forces electrons to jump up from the
valence band and become free electrons in the conduction band, leaving behind a hole. The top layer, the n-
type layer, was intentionally made very thin, so very little light is absorbed there. The space charge regions on
either side of the junction are also very thin, and the light absorbed in them is also small.
Most of the light (we hope) gets through to the p-type layer, and this is where the interesting things happen.
Using our previous example, suppose we have enough light to increase the concentration of free electrons to
1011cm-3. This is an increase by a factor of one million. The concentration of holes also goes up by the same
amount, but it is trivial compared to the 1015 holes/cm3 we already have.
Some of our newly free optically generated electrons wander over near the space charge region, where they feel
the pull of the positively charged phosphorus atoms on the other side of the junction, and these free electrons
go across. They then manage to make their way across the thin n-type region and out of the solar cell, and
become part of the current in the solar cell’s circuit. They are compensated for by electrons that go in the back
end of the p-type region and recombine with holes there. Over all, the solar cell still remains charge neutral.
Since the pull of the phosphorus atoms maintains a low concentration of electrons near the p-type side’s space
charge region, optically generated free electrons deeper inside the p-type region keep wanting to diffuse toward
the junction.
It’s all pretty complicated, but it really works. And from this, we get the PV industry.
An important concept we have encountered is that free electrons and holes behave pretty much the same. This
is sometimes called electron-hole symmetry. Holes really act like positively charged particles. When this author
took his first course on this material, the professor was said to be founding a religion based on belief in the
existence of the hole. We found it hard to believe, too.
We could make a solar cell which is mainly n-type and has a thin p-type layer on top, reversing the one described
above. At least one company makes solar cells this way. But the more common way, at least for crystalline
silicon solar cells, is as described above. There are many reasons that we have skipped over, including
manufacturing cost, that determine how people choose to make solar cells. One commentator on the PV
industry recently wrote that he expects solar cells that are primarily n-type with a thin p-type layer at the top to
capture a larger market share in 2011. He didn’t explain the reasons for his prediction. We’ll see what happens.
The solar cell design we have discussed here is a relatively simple one, but is very close to the design of many
solar cells on the market. More complicated designs are used for some more expensive solar cells. We have
seen a diagram of a more complicated solar cell made by SunPower.
While we’re at it, we’ll spend a moment on how amorphous silicon solar cells work. Much of what we wrote
above for crystalline silicon is about the same for amorphous silicon, except that amorphous silicon is an
amorphous thin film. Instead of a relatively thin n-type layer adjacent to a thicker p-type layer (or vice versa),
amorphous silicon solar cells usually have a thin p-type layer and a thin n-type layer, with a thicker undoped
layer (called an intrinsic layer, or i-layer) in between. There is a space charge layer at the junction of the p and i
layers, and one at the junction of the i and n layers. When light is shined on the solar cell, most of it is absorbed
in the thicker i-layer. The free electrons generated are attracted by the positive space charge in the n-type layer,
and the holes generated are attracted by the negative space charge in the p-type layer. Some of the electrons
and holes recombine before they make it out of the i-layer, but if they do make it they can become part of the
current in the circuit.