What is solar cell or photovoltaic cell?
Solar
cell also known as photo voltaic cell is a electronic device which
converts light (photo) energy of sun into electrical energy. It is the
basic building block of every solar power plant.. It works on the
principle of photo voltaic effect.
Symbol of solar cell
The symbol of solar cell is shown in the figure below
Principle of operation of solar cell
if light falls on the surface of a open circuited PN junction, the incident photons can undergo following possibilities
- Reflection of the incident material surface
- Refraction, it will pass through the material without any interaction
- Absorption, the photons gets absorbed by electron in valence band.
When
photons are absorbed by the electrons in valence band photo generation
takes place i.e. hole electron pairs are generated. The electrons in
valance band will gain energy by absorbing photonic or light energy and
are excited to conduction band by leaving a hole in valence band. Hence
for each photo excitation two charge carriers are produced hole in
valence band and electron in conduction band.
Due
to potential barrier developed across the junction no holes are allowed
to flow from p side to n side, similarly no electrons are allowed to
floe from n side to p side.
If
photo generation takes place within one diffusion length the minority
carriers has high probability that they will cross the junction. Since
minority carriers are allowed fall down the junction barrier the
minority carrier current increases. Under open circuited junction the
total current through the junction should be zero. So the majority
current should also increase in line with the minority carrier current
so that the net current through the junction is zero. The rise in
majority carrier current is possible only because of a retarding field
which lower the barrier height. Hence the barrier height is
automatically lowered due to radiation. Across the diode terminals there
appears a voltage equal to the amount by which the barrier height is
reduced. This voltage is called photo voltaic EMF and the effect is
termed as photo voltaic effect.
Current components in an ideal solar cell
Consider
a solar cell connected to a load as shown in figure. As light falls on
solar cell photo current travels from n side to p side in addition to
minority saturation current. The solar cell will be reverse biased for
its entire operation. The reverse bias voltage across the photovoltaic
cell depends on current though it. Hence the current in a solar cell
consists of two components
- Photo current
- Minority current
Therefore the total current It = Iph + Im
where Iph is photo current,
Im is minority carrier current.
where Iph is photo current,
Im is minority carrier current.
Photo current
The
photo current is due to diffusion or drift of photo generated carriers
across the junction. This photo current almost varies linearly with the
incident light flux. Across the junction there exists two mechanisms by
which photo generated carriers flow through the junction.
Diffusion
currents are due to statistical random thermal motion of charge
carriers and charge gradient. Diffusion current are proportional to
charge gradients (charge gradient is the variation of charge
concentration with respect to distance). In thick solar cells the
diffusion length will be greater than the cell thickness, hence the
diffusion current dominates.
Drift
currents due to force applied by electric field (established across the
surface) on the carriers. In thin film solar cells drift currents
dominates.
Minority carrier current
The
minority carrier current is similar to what we observe in a reverse
biased PN junction diode. It is due to diffusion of holes on n side to p
side and electrons from p side to n side. The current equation of a
diode is given as
Id = Io*(e V/ (η*Vt)-1)
Where
η is 1 for Ge and 2 for Si, Vt is voltage equivalent of temperature, V
is positive for forward bias and negative for reverse bias. Io is
reverse saturation current of diode and is given as
I0 = A*Vt*a*σi2*(1/ (Lp*σn) +1/ (Ln*σn))/ (1+b)2
Where A = area of cross section of semiconductors,
b = µn/ µp,
µp and µn are the mobilities of holes and electrons,
Lp and Ln are diffusion lengths for holes and electrons,
σi is the intrinsic concentration of semiconductors,
σn and σp are conductivities of n type and p type semiconductors.
b = µn/ µp,
µp and µn are the mobilities of holes and electrons,
Lp and Ln are diffusion lengths for holes and electrons,
σi is the intrinsic concentration of semiconductors,
σn and σp are conductivities of n type and p type semiconductors.
When
the reverse bias across the solar cell is very much less compared to Vt
i.e. at least V(reverse bias) < -5*Vt, eV/ (η*Vt) tends to zero then
the diode current tends to –Io independent of applied bias.
Hence
the total current in solar cell is given as I = – (Iph + Io). The
negative sign indicates current flow from n side to p side.
Solar Cell or Photo Voltaic cell efficiency
There are two types of quantum efficiency of a solar cell
External Quantum Efficiency (E.Q.E)
is the ratio of the number of charge carriers collected by the solar
cell to the number of incident photons of a given energy shining on the
solar cell from outside.
Internal Quantum Efficiency (I.Q.E)
is the ratio of the number of charge carriers collected by the solar
cell to the number of photons of a given energy that shine on the solar
cell from outside and are absorbed by the cell.
The
IQE is always larger than the EQE as some of the photons incident on
the solar cell may got reflected, refracted though the material. The
total photons incident on solr cell is given as
Ntotal = Nreflected+Nrefracted+Nabsorbed
Total Absorption= Nabsorbed/Ntotal = (Ntotal- Nreflected-Nrefracted)/Ntotal = 1-Reflection-Transmission.
External quantum efficiency = (photo current/charge of one electron)/(incident light power/Energy of one photons).
I.Q.E = E.Q.E/Total absorption
The
external quantum efficiency therefore depends on both the absorption of
light and the collection of charges. Once a photon has been absorbed
and has generated an electron-hole pair, these charges must be separated
and collected at the junction. A good material avoids charge
recombination. Charge recombination causes a drop in the external
quantum efficiency.
The relation between the Responsivity and external quantum efficiency is given as
External quantum efficiency = (I/e)/(Pin/ h*ν)
Since R = I/Pin hence Q = R*h*ν/e and
Where R is Responsivity,
Q is Quantum efficiency,
h is Planck’s constant,
ν is frequency of incident photon,
Energy of h*ν photon = h*ν,
Iph is photo generated current,
Pin is incident optical power.
Hence the total current in a photo voltaic cell is given as
It = Io*(eV/ (η*Vt)-1) -Q*e*Pin/(h*v)
Q is Quantum efficiency,
h is Planck’s constant,
ν is frequency of incident photon,
Energy of h*ν photon = h*ν,
Iph is photo generated current,
Pin is incident optical power.
Hence the total current in a photo voltaic cell is given as
It = Io*(eV/ (η*Vt)-1) -Q*e*Pin/(h*v)
IV characteristics of solar cell
The IV characteristics of TiO2 Coated Carbon Nano tube Silicon Solar Cells is shown in the figure below
From
the characteristics it is obvious that for no illumination there exist
no currents flowing though solar cell except for minority carrier
current also termed as dark current. The dark and illuminated J-V
characteristics of the p-n junction are represented in Figure. Note,
that the superposition principle is reflected in Figure4.10. The
illuminated J-V characteristic of the p-n junction is the same as the
dark J-V characteristic, but it is shifted down by the photo-generated
current density Jph.
Single diode Equivalent circuit model of ideal solar cell
The
solar cell is a current source which allows photo current to flow
through it if the circuit containing it is closed. From the theory
presented above the ideal equivalent circuit of solar cell as follows
Where Iph is photo current, Id = Io*(eV/ (η*Vt)-1) ~ -Io.
Single diode Equivalent circuit model of practical solar cell
A practical solar cell suffers from so many practical losses which can be accounted for in the model of solar cell by adding two resistances 1) series resistance and 2) shunt resistance
Series resistance represents the bulk resistance of the semiconductor materials, resistance of metal contacts and the resistance of interface between semiconductor and metal contacts. The series resistance as the name suggests is connected in series with current source and diode.
Shunt resistance accounts for current losses in the semiconductor. It is connected in parallel to photo current source and diode. The practical real non ideal equivalent circuit model of solar cell is shown in the figure
Where Iph is photo current, Id = Io*(eV/ (η*Vt)-1) ~ -Io.
Single diode Equivalent circuit model of practical solar cell
A practical solar cell suffers from so many practical losses which can be accounted for in the model of solar cell by adding two resistances 1) series resistance and 2) shunt resistance
Series resistance represents the bulk resistance of the semiconductor materials, resistance of metal contacts and the resistance of interface between semiconductor and metal contacts. The series resistance as the name suggests is connected in series with current source and diode.
Shunt resistance accounts for current losses in the semiconductor. It is connected in parallel to photo current source and diode. The practical real non ideal equivalent circuit model of solar cell is shown in the figure
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