Solar Cells

A solar cell is a device that transforms the solar power that is incident on its surface into electric power available for use in an external electric circuit that contains a load. The primary principle that makes a solar cell working is the internal photoelectric effect that is similar to the external photoelectric effect for which Einstein has got his Nobel Price. Both these effects take place when a light photon strikes an electron from a solid material atom (be it a metal or semiconductor). If the energy of the incoming photon is big enough the electron will be expelled from the atom leaving behind an empty place (named a hole if the material is a semiconductor). If the electron is expelled from the surface of the material (when light strikes an atom from the surface) the effect is called external, if the photon travels a certain distance into the material and the electron is expelled from the bulk of the material the effect is called internal photoelectric effect.
  Therefore as a result of light exposure, a pair electron-hole is created into the bulk of the semiconductor from which the solar cell is made up. Normally, if there is no other additional factor to act upon the electron-hole pair, after a short time the electron will get back into its place (it is said that the electron and hole will recombine). But a solar cell is made up of a p-n junction of two differently doped semiconductors. In the junction region, an internal electric field builds up because of the junction asymmetry (different doping). If the electron-hole pair is generated by the photon in this region (of the p-n junction) the existent internal electric field will split apart the electron from the hole driving them in opposite directions. (It is said that an electric drift current will happen). When they will exit the p-n junction region at its opposite ends (which is just a region having a small extent in the semiconducting device), the electron and the hole will continue to travel by pure diffusion until they arrive at the physical endings of the semiconductor, where they will be extracted by two metallic contacts. Therefore this length of the neutral parts of the semiconductor (outside the p-n junction) needs to be smaller than the diffusion length of the charge carriers (a value characteristic to each semiconductor). Also each material has a light absorption length (the length where the intensity of the light decreases by a factor of “e”), and therefore the semiconductor needs to be at the same time thicker than this light absorption length.
What we said before about how a solar cell works, gives a good idea about how a solar cell is constructed. Between two electrodes (the upper electrode which needs to be transparent for most light wavelengths and the lower electrode that needs to be reflecting for light), there is a “sandwich” made up from two different doped regions of the same semiconductor. The interface between the two regions (p and n) that is making up the p-n junction is engineered in such way that a good part of the available light will be absorbed and will generate electron-hole pairs. This involves in principal choosing a semiconductor material having a direct band gap (minim of conduction band corresponds in momentum space to maxim of valence band) which energy is lower than the smaller energy of the available photons. Early solar cells were built based on a metal-semiconductor junction (Schottky junction) between one electrode (usually the surface electrode) and the semiconductor, not on a p-n junction in the semiconductor bulk. “Standard” steps in the manufacturing of a “classical” solar cell are purifying the Silicon, growing the single Silicon crystal, cutting the Silicon wafers from the single crystal, doping the wafer to obtain the p-n junction inside it, depositing the contacts and finally encapsulating the structure. However during the last years, because of the new materials available for making solar cells (apart from Silicon) and of new technologies that have been developed, the manufacture of a solar cell can involve other different procedures. 
 When it comes to the material the solar cells are made of, Silicon is the wide used and accepted semiconductor. It has a direct (see the explanation above) band gap of 1.12 eV and a good light absorption coefficient that allows the solar cells to have a thickness of just a 100-150 microns. Silicon semiconductor can be of many types in recent solar cells. Progresses in materials physics have made available also other semiconductors for solar cells like for example CdTe, InP or GaAs that are binary compound semiconductors of the type AIIIBV or AIIBVI. However Silicon is still the most widely used material even today. Very recent solar cells are made using semiconductor colloidal quantum dots, a technique that promises very cheap solar cells.
The price of the electrical power generated by using solar cells is nowadays about 30-40 cents (USD) per watt. These solar cells can be easily bought from online auction sites like Alibaba, or Ebay.  
The efficiency of a solar cell is defined as the report between the electrical power generated to the incident solar power on the cell surface. The first solar cells had an efficiency of about 1%, while today usual solar cells have efficiencies of about 20% and above. Recently (2014-2015) there for single junction solar cells have been reported efficiencies of 25% or even a bit higher (The theoretical maximum efficiency for a single junction solar cell is around 33%. This means that from 1 square meter solar cell area one can harvest a maximum of about 250-300 W of electric power). The main technique to improve the efficiency of the solar cells is to use a sandwich of solar cells one after another, each of the solar cells being engineered in such a way that it absorbs light from different parts of the spectrum. To achieve this variable band gap semiconductors are necessary like Al(x)Ga(1-x)As or quantum dots of a certain size. Since each solar cell from the sandwich will absorb a different portion of the light spectrum, being connected in series (in a sandwich pack) the overall efficiency will increase over the theoretical limit of 33%. Up to now efficiencies of up to 40% have been reported. Other techniques for increasing solar cell efficiency consist of changing the shape of solar cell (like cylindrical solar cells), heating the surface of the solar cell (using hot water for example to control the semiconductor  temperature), sun tracking, or even light focusing by lenses in front of solar cells.
As shown above, the main parameter that determines the absorption of light is the band gap of the semiconductor used. Taking Silicon for example having band gap of 1.12 eV, this is the lowest photon energy that is absorbed. This corresponds to a wavelength of  hc/λ=E , or λ≈1100 nm=1.1 μm which is into the infrared spectrum.  All light having shorter wavelengths will be absorbed into the solar cell, but the absorption coefficient will depend again on the wavelength. Basically blue light is absorbed near the surface of the solar cell (it has a stronger absorption coefficient) while infrared (up to to 1100 μm) can travel well beyond the structure thickness before being theoretically absorbed. This is called the spectral response of the solar cell. A basic law of the solar cell is that the spectral response (SR) of a cell depends on the quantum efficiency multiplied with the wavelength of the light (the quantum efficiency QE shows how many electron-hole pairs are generated for a given number of incident photons). Thus
The “open circuit” voltage generated by the solar cell will correspond to the p-n junction “built-in potential” which is about 0.5-1 V depending on the material type (typical built in voltage for a Si p-n junction is 0.7 V). On a short circuit, the current generated will depend on the quantity of the light absorbed and on the efficiency of the cell. For a few cm^2 of area, a typical short circuit current is about 10-50 mA.  Therefore to achieve an electrical power at the level necessary for a household groups of series-parallel solar cells need to be used in practise. For example for a house consuming an average of 2Kw electrical power, using solar cells of a 20% total efficiency, the power of the sun light necessary to illuminate the solar cells will be 10 kW. Since at noon in the summer the available sun power si 900-1000 W/square meter, for this house there will be necessary an area of 10 square meters covered with solar cells.