Solar cell: Encyclopedia II - Solar cell - Theory

Solar cell - Theory

Solar cell - Background

In order to understand how a solar cell works, a little background theory in semiconductor physics is required. For simplicity, the description here will be limited to describing the workings of single crystalline silicon solar cells.

Silicon is a group 14 (formerly, group IV) atom. This means that each Si atom has 4 valence electrons in its outer shell. Silicon atoms can covalently bond to other silicon atoms to form a solid. There are two basic types of solid silicon, amorphous (having no long range order) and crystalline (where the atoms are arranged in an ordered three dimensional array). There are various other terms for the crystalline structure of silicon; poly-crystalline, micro-crystalline, nano-crystalline etc, and these refer to the size of the crystal "grains" which make up the solid. Solar cells can be, and are made from each of these types of silicon, the most common being poly-crystalline.

Silicon is a semiconductor. This means that in solid silicon, there are certain bands of energies which the electrons are allowed to have, and other energies between these bands which are forbidden. These forbidden energies are called the "band gap". The allowed and forbidden bands of energy are explained by the theory of quantum mechanics.

At room temperature, pure silicon is a poor electrical conductor. In quantum mechanics, this is explained by the fact that the Fermi level lies in the forbidden band-gap. To make silicon a better conductor, it is "doped" with very small amounts of atoms from either group 13 (III) or group 15 (V) of the periodic table. These "dopant" atoms take the place of the silicon atoms in the crystal lattice, and bond with their neighbouring Si atoms in almost the same way as other Si atoms do. However, because group 13 atoms have only 3 valence electrons, and group 15 atoms have 5 valence electrons, there is either one too few, or one too many electrons to satisfy the four covalent bonds around each atom. Since these extra electrons, or lack of electrons (known as "holes") are not involved in the covalent bonds of the crystal lattice, they are free to move around within the solid. Silicon which is doped with group 13 atoms (aluminium, gallium) is known as p-type silicon because the majority charge carriers (holes) carry a positive charge, whilst silicon doped with group 15 atoms (phosphorus, arsenic) is known as n-type silicon because the majority charge carriers (electrons) are negative. It should be noted that both n-type and p-type silicon are electrically neutral, i.e. they have the same numbers of positive and negative charges, it is just that in n-type silicon, some of the negative charges are free to move around, while the converse is true for p-type silicon.

Solar cell - Light generation of carriers

When a photon of light hits a piece of silicon, one of two things can happen. The first is that the photon can pass straight through the silicon. This (generally) happens when the energy of the photon is lower than the bandgap energy of the silicon semiconductor. The second thing that can happen is that the photon is absorbed by the silicon. This (generally) happens if the photon energy is greater than the bandgap energy of silicon. When a photon is absorbed, its energy is given to an electron in the crystal lattice. Usually this electron is in the valence band, and is tightly bound in covalent bonds between neighboring atoms, and hence unable to move far. The energy given to it by the photon "excites" it into the conduction band, where it is free to move around within the semiconductor. The covalent bond that the electron was previously a part of now has one less electron - this is known as a hole. The presence of a missing covalent bond allows the bonded electrons of neighboring atoms to move into the "hole," leaving another hole behind, and in this way a hole can move through the lattice. Thus, it can be said that photons absorbed in the semiconductor create mobile electron-hole pairs.

A photon only needs to have energy greater than the band gap energy to excite an electron from the valence band into the conduction band. However, the solar frequency spectrum approximates a black body spectrum at ~6000 K, and as such, much of the solar radiation reaching the Earth is composed of photons with energies greater than the band gap of silicon. These higher energy photons will be absorbed by the solar cell, but the difference in energy between these photons and the silicon band gap is converted into heat (via lattice vibrations - called phonons) rather than into usable electrical energy.

Solar cell - The p-n junction

A solar cell is a large-area semiconductor p-n junction. To understand the workings of a p-n junction it is convenient to imagine what happens when a piece of n-type silicon is brought into contact with a piece of p-type silicon. In practice, however, the p-n junctions of solar cells are not made in this way, but rather, usually, by diffusing an n-type dopant into one side of a p-type wafer.

If we imagine what happens when a piece of p-type silicon is placed in intimate contact with a piece of n-type silicon, then what occurs is a diffusion of electrons from the region of high electron concentration - the n-type side of the junction, into the region of low electron concentration - p-type side of the junction. When the electrons diffuse across the p-n junction, they recombine with holes on the p-type side. This diffusion of carriers does not happen indefinitely however, because of the electric field which is created by the imbalance of charge immediately either side of the junction which this diffusion creates. Electrons from donor atoms on the n-type side of the junction are crossing into the p-type side, leaving behind the (extra) positively charged nuclei of the group 15 donor atoms, leaving an excess of positive charge on the n-type side of the junction. At the same time, these electrons are filling in holes on the p-type side of the junction, becoming involved in covalent bonds around the group 13 acceptor atoms, making an excess of negative charge on the p-type side of the junction. This imbalance of charge across the p-n junction sets up an electric field which opposes further diffusion of charge carriers across the junction.

This region where electrons have diffused across the junction is called the depletion region because it no longer contains any mobile charge carriers. It is also known as the "space charge region".

The electric field which is set up across the p-n junction creates a diode, allowing current to flow in only one direction across the junction. Electrons may pass from the n-type side into the p-type side, and holes may pass from the p-type side to the n-type side. But since the sign of the charge on electrons and holes is opposite, conventional current may only flow in one direction.

Solar cell - Separation of carriers by the p-n junction

Once the electron-hole pair has been created by the absorption of a photon, the electron and hole are both free to move off independently within the silicon lattice. If they are created within a minority carrier diffusion length of the junction, then, depending on which side of the junction the electron-hole pair is created, the electric field at the junction will either sweep the electron to the n-type side, or the hole to the p-type side.

Solar cell - Connection to an external load

Ohmic metal-semiconductor contacts are made to both the n-type and p-type sides of the solar cell, and the electrodes connected to an external load. Electrons that are created on the n-type side, or have been "collected" by the junction and swept onto the n-type side, may travel through the wire, power the load, and continue through the wire until they reach the p-type semiconductor-metal contact. Here, they recombine with a hole that was either created as an electron-hole pair on the p-type side of the solar cell, or swept across the junction from the n-type side after being created there.

Solar cell - Equivalent circuit of a solar cell

To understand the electronic behaviour of a solar cell, it is useful to create a model which is electrically equivalent, and is based on discrete electrical components whose behaviour is well known. An ideal solar cell may be modelled by a current source in parallel with a diode. In practice no solar cell is ideal, so a shunt resistance and a series resistance component are added to the model. The result is the "equivalent circuit of a solar cell" shown on the left. Also shown on the right, is the schematic representation of a solar cell for use in circuit diagrams.

Adapted from the Wikipedia article "Theory", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki