solar cell or photovoltaic cells operation and efficiency

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

Solar Cell Symbol

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.

band diagram of solar cell

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.

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.

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)

IV characteristics of solar cell

The IV characteristics of TiO2 Coated Carbon Nano tube Silicon Solar Cells is shown in the figure below

Nano tube Silicon Solar Cell JV characteristics

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

practical solar cell equivalent circuit