Exercises on Photovoltaic 1) What are a) the Fermi level, b) the conduction band and c) the valence band?

a) Fermi level is the energy level of an atom in a solid at a given temperature for

which there is a 50 percent probability of occupation of any available state of that

energy by an electron.

b) The conduction band is the range of electron energies enough to free an electron

from binding with its atom to move freely within the atomic lattice of the material as a

'delocalized electron'. Various materials may be classified by their band gap: this is

defined as the difference between the valence and conduction bands.

• In non-conductors, aka insulators, the conduction band is higher than that of

the valence band, so it takes in feasibly high energies to delocalize their

valence electrons. They are said to have a non-zero band gap.

• In conductors, such as metals, that have many free electrons under normal

circumstances, the conduction band overlaps with the valence band--there is

no band gap.

• In semiconductors, the band gap is small. This explains why it takes a little

energy (in the form of heat or light) to make semiconductors' electrons

delocalize and conduct electricity, hence the name, semiconductor.

Electrons within the conduction band are mobile charge carriers in solids,

responsible for conduction of electric currents in metals and other good

electrical conductors.

c) In solids, the valence band is the highest range of electron energies in which

electrons are normally present at absolute zero temperature.

The valence electrons are bound to individual atoms, as opposed to

conduction electrons (found in conductors and semiconductors), which can

move freely within the atomic lattice of the material. On a graph of the

electronic band structure of a material, the valence band is located below the

conduction band, separated from it in insulators and semiconductors by a

band gap. In metals, the conduction band has no energy gap separating it

from the valence band.

2) What is the band gap of silicon?

The band gap of silicon is 1.14 eV.

3) Explain the principle of a p-n junction with reference to the depletion region.

4) Explain the generation of electricity in a solar cell.

In a solar cell, we connect a positive and negative doped semiconductor to create a

pn junction. These connections create an intrinsic electric field with the processes of

drift and diffusion. When a photon is incident in the depletion region, if there is

enough energy above the difference between the conduction and the valence band,

an electron and a hole will be generated. Then the electric field will move the

carriers that are generated from the incident photons, preferable through the metal

contacts that offer lesser resistance than the resistance through the pn junction and

thereafter through the load to generate electricity.

5) Draw and explain the structure of a PV cell.

The bottom contact is the substrate at which the PV cell resides. The textured surface is there to trap the incident light and force it to go through the p-n junction. Beneath the textured surface, there is the n-type also called emitter, and beneath it, there is the p-type material also called donor. At the interface between the n-type and p-type semiconductors, we have the formation of the pn junction and of the depletion region, which is formed by diffusion and drift processes. The burried contacts are used as electrodes to be connected either to the load or to another PV cell.

6) What are the typical efficiencies of monocrystalline, polycrystalline silicon cells,

and non-silicon cells?

Polycrystalline Solar Panels

Under standard conditions their conversion efficiency of sunlight to electricity is

12% to 12.5%,

Monocrystalline Solar Panels

Under standard conditions their conversion efficiency of sunlight to electricity is

12% to 15%,

Amorphous modules

Their conversion efficiency of sunlight to electricity is 6.3%, about half that of

polycrystalline or monocrystalline panels.

Thin films GaAs Their conversion efficiency of sunlight to electricity is 30-40%.

Thin films CIGS Their conversion efficiency of sunlight to electricity is 20%.

Thin films CdTe Their conversion efficiency of sunlight to electricity is 15%.

7) Draw the current-voltage graph of a typical photovoltaic module and explain the

concepts of short circuit current, open circuit voltage and maximum power point.

8) State 4 drawbacks and 4 advantages of photovoltaics.

9) The band gap of GaAs is 1.4 eV. Calculate the optimum wavelength of light for

photovoltaic generation in a GaAs solar cell.

10) a) Give the equation for the I–V characteristic of a p–n junction diode in the dark.

b) If the saturation current is 10−7 Am−2, calculate and draw the I–V characteristic

plotting the curve values at voltages of -∞, 0, 0.1 and 0.2 V

11) a) What is the approximate photon flux density (photon s−1 m−2) for AM1 solar

radiation at 0.8 kWm−2?

b) AM1 insolation of 0.8kWm−2 is incident on a single Si solar cell of area 100 cm2.

Assume 10% of photons cause electron–hole separation across the junction leading

to an external current. What is the short circuit current Isc of the cell? Sketch the I–V

characteristic for the cell.

12) a) Design a suitable photovoltaic power system that will charge the battery from

an arrangement of Si solar cells by making reference of how you expect to arrange

the PV cells? (Assume current density of a single solar cell is 200 x 10-4 Acm-2, 22 V

are enough to charge the battery, and that we have 2 hours of direct sunlight each

day).

b) How will you test the circuit and performance?

13) What is the best fixed orientation for power production from a photovoltaic

module located at the South Pole?

The best fixed orientation for a photovoltaic module is to be place facing downwards

such that it is using the reflected light from the snow to produce electrical energy

without being affected by the snow.

14) Einstein won the Nobel Physics Prize in 1905 for explaining the photoelectric

effect, in which light incident on a surface can lead to the emission of an electron

from that surface with energy:

E = hν−Φ

where hν is the energy of a photon of light and Φ is a property of the surface.

a) What are the main differences and similarities between the photoelectric effect

and the photovoltaic effect?

In both the photoelectric and photovoltaic effect we have the generation of free

carriers, with the photoelectric effect having produced charges mostly in metals

which exist in solids (holes) and free electrons in air, i.e. in separate mediums,

whereas electrons and holes are generated only in semiconductors and remain in

the same medium. The difference in the two effects is that the photovoltaic effect

has an intrinsic electric field which is able to generate electricity, which does not

exist in the photoelectric effect. The only current of the photoelectric effect comes

from the motion of the electrons which is very small.

b) Discuss how, if at all, the photoelectric effect could be used to yield useful energy.

The photoelectric effect generates charges, however their speed is very low and

cannot produce significant amount of energy, however it can be used for generating

charges i.e. as a source of charge carriers.

15) The band gap of intrinsic Si at 29 OC is 1.14 eV. Calculate the probability

function exp�(−Eg/2kT) for electrons to cross the full band gap by thermal

excitation.

16) A Si photovoltaic module is rated at 200W with insolation 1000Wm−2 as for peak

insolation on Earth. What would be its peak output on Mars? (Data: Mean distance

of the Sun from Earth is 1.50×1011 m; from Mars 2.28×1011 m.

17) Imagine a family living in Africa. They have no grid connection and hence no

electricity so they intend to buy a Solar Home System (SHS). This will allow them to

have light and to watch TV in the evening. You must help them to look at their

electricity requirement to see what size of SHS will provide enough electricity.

In Africa, where their home is, the energy from the sun averages 6 kWh/m2 each

day. That means the energy provided from the sun is equivalent to a light intensity of

1000W/m2 for six hours each day. In fact there would be about 12 hours of sunlight

during which time the light intensity would vary but the daily total would be 6

kWh/m2.

(a) The PV module in a SHS has a power output of 50 Wp. Assuming that the

module operates at 25°C (i.e. at STC), how much electricity will it provide every

day?

(b) The family wants to have one light in the main room of the house, one light in the

kitchen and one on a table where the children do their homework. Of course they

would use low energy light bulbs, which require between seven and twenty Watts.

(Equivalence of low energy light bulbs to standard light bulbs: 7 W @ 40 W, 11 W @

60 W, 16 W @ 75 W & 20 W @ 100 W).

Which light bulbs would it be best to use for the different lamps and why?

(c) Assume that the main light is used for four hours a day, the kitchen light for two

hours per day and the table light for three hours each day. How much electrical

energy does each light use each and what is the total daily requirement of the

lights? What power output would a PV module require to supply this electricity?

(d) The family also likes to watch TV. If their television requires 50 W and they watch

every day for two hours, what is its daily electrical energy requirement?

(e) Does the PV module in the SHS supply enough energy for all their needs?

(f) Discuss the result.