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In physicssingle landsberg Shockley—Queisser limit also known as the detailed balance limitShockley Queisser Efficiency Limit or SQ Limitor in physical terms the radiative efficiency limit is the maximum theoretical efficiency of a solar cell using a single p-n junction to collect power from the cell where the only loss mechanism single landsberg radiative recombination in the solar cell, single landsberg.
Subsequent calculations have used measured global solar spectra AM1. The limit is that the maximum solar conversion efficiency is around This maximum occurs at a band gap of 1. The most popular solar cell material, silicon, single landsberg a less favorable band gap of 1. The Shockley—Queisser limit only applies to conventional single landsberg cells with a single p-n junction; solar cells with multiple layers can and do outperform this limit, and so can solar thermal and certain other solar energy systems.
In the extreme limit, for a multi-junction solar cell with an infinite number of layers, the corresponding limit is In a traditional solid-state semiconductor such as silicona solar cell is made from two doped crystals, one single landsberg n-type semiconductorwhich has extra free electrons single landsberg, and the other a p-type semiconductorwhich is lacking free electrons, referred to as " holes.
Eventually enough will flow across the boundary to equalize the Fermi levels of the two materials. The result is a region at the interface, the p-n junctionwhere charge carriers are depleted on each side of the interface. In silicon, this transfer single landsberg electrons produces a potential barrier of about 0. When the material is placed in the sun, photons from the sunlight can be absorbed in the p-type side of the semiconductor, causing electrons in the valence band to be promoted in energy to the conduction band.
This process is known as photoexcitation. As the name implies, electrons in the conduction band are free to move about the semiconductor.
When a load is placed across the cell as a whole, these electrons will flow from the p-type side into the n-type side, lose energy while moving through the external circuit, and then go back into the p-type material where they can re-combine with the valence-band holes they left behind. In this way, sunlight creates an electric current. The Shockley—Queisser limit is calculated by examining the amount of electrical energy that is extracted per photon of incoming sunlight.
There are several considerations:. Any material, that is not at absolute zero 0 Kelvinemits electromagnetic radiation through the black-body radiation effect, single landsberg. Any energy lost in a cell is turned into heat, so any inefficiency in the cell increases the cell temperature when it is placed in sunlight. As the temperature of the cell increases, the outgoing radiation and heat loss through conduction and convection also increase, until an equilibrium is reached.
In practice, single landsberg, this equilibrium is normally reached at temperatures as high as Kelvin, and consequently, single landsberg, cells normally operate at lower efficiencies than their room-temperature rating, single landsberg.
Module datasheets normally list this temperature dependency as T NOCT NOCT - Nominal Operating Cell Temperature. For a "blackbody" at normal temperatures, a very small part of this radiation the number per unit time and per unit area given by Q c"c" for "cell" is photons having energy greater than the band gap wavelength less than about 1.
This is a very small effect, but Shockley and Queisser assume that the total rate of recombination see below when the voltage across the cell is zero short circuit or no light is single landsberg to the blackbody radiation Q c. This rate of recombination plays a single landsberg role in the efficiency.
Shockley and Queisser calculate Q c to be photons per second per square centimetre for silicon at K. Absorption of a photon creates an electron-hole pair, which could potentially contribute to the current. However, the reverse process must also be possible, according to the principle of detailed balance : an electron and a hole can meet and single landsberg, emitting a photon.
This process reduces the efficiency of the cell, single landsberg. Other recombination processes may also exist see "Other considerations" belowbut this one is absolutely required. In the Shockley—Queisser model, the recombination rate depends on the voltage across the cell single landsberg is the same whether or not there is light falling on the cell. The factor of 2 was included on the assumption that radiation emitted by the cell goes in both directions.
This is actually debatable if a reflective surface is used on the shady side. q being the charge of an electron. This is actually an approximation, correct so long as the cell is thick enough to act as a black body, to the more accurate expression [7] [8]. The difference in maximum theoretical efficiency however is negligibly small, except for tiny bandgaps below meV. The rate of generation of electron-hole pairs not due to incoming sunlight stays the same, so recombination minus spontaneous generation is.
Shockley and Queisser take f c to be a constant, although they admit that it may single landsberg depend on voltage, single landsberg. This rate of generation is called I sh because it is the "short circuit" current per unit area. When there is a load, single landsberg, then V will not be zero and we have a current equal to the rate of generation of pairs due to the sunlight minus the difference between recombination and spontaneous generation:. The open-circuit voltage is therefore given assuming f c does not depend on voltage by.
The product of the short-circuit current I sh and single landsberg open-circuit voltage V oc Shockley and Queisser call the "nominal power". It is not actually possible to get this amount of single landsberg out of the cell, but we can get close see "Impedance matching" below.
The ratio of the open-circuit voltage to the band-gap voltage Shockley and Queisser call V. Under open-circuit conditions, we have. where V s is the voltage equivalent of the temperature of the sun. This is why single landsberg efficiency falls if the cell heats up.
In fact this expression represents the thermodynamic upper limit of the amount of work that can be obtained from a heat source at the temperature of the sun and a heat sink at the temperature of the cell. Since the act single landsberg moving an electron from the valence band to the conduction band requires energy, only photons with more than that amount of energy will produce an electron-hole pair.
In silicon the conduction band is about 1. In other words, photons of red, yellow and blue light and some near-infrared will contribute to power production, single landsberg radio waves, microwaves, and most infrared photons will not. Another important contributor to losses is that any energy above and beyond the bandgap energy is lost. While single landsberg light has roughly twice the energy of red light, that energy is not captured by devices with a single p-n junction.
The electron is ejected with higher energy when struck by a blue photon, but it loses this extra energy as it travels toward the p-n junction the energy is converted into heat. There is a trade-off in the selection of a bandgap. If the band gap is large, not as many photons create pairs, whereas if the band gap is small, the electron-hole pairs do not contain as much energy, single landsberg.
Shockley and Queisser call the efficiency factor associated with spectrum losses ufor "ultimate efficiency function". Shockley and Queisser calculated that the best band gap for sunlight happens to be 1. They single landsberg blackbody radiation of K for sunlight, and found that the optimum band gap would then have an energy of 2. Using a more accurate spectrum may give a slightly different optimum.
If the resistance of the load is too high, the current will be very low, while if the load resistance is too low, single landsberg, the voltage drop across it will be very low. There is an optimal load resistance that will draw the most power from the solar cell at a given illumination level. Shockley and Queisser call the ratio of power extracted to I sh V oc the impedance matching factor, m.
It is also called the fill factor. The optimum depends on the shape of the I versus V curve. But for high illumination, m approaches 1.
Shockley and Queisser give a graph showing m as a function of the ratio z oc of the open-circuit voltage to the thermal voltage V c, single landsberg. Using the above-mentioned values of Q s and Q csingle landsberg, this gives a ratio of open-circuit voltage to thermal voltage of The authors derive the equation.
which can be solved to find z msingle landsberg, the ratio of optimal voltage to thermal voltage. One can then use the formula. to find the single landsberg matching factor. Thus the spectrum losses represent the vast majority of lost power. Including the effects of recombination and the I versus V curve, the efficiency is described by the following equation:.
where uvand m are respectively the ultimate efficiency factor, single landsberg, the ratio of open-circuit voltage V op to band-gap voltage V gand the impedance matching factor all discussed aboveand V c is the thermal voltage, and V s is the voltage equivalent of the temperature of the Sun, single landsberg.
A more recent reference gives, for a single-junction cell, a theoretical peak performance of about When the amount of sunlight is increased using reflectors or lenses, the factor f ω and therefore f will be higher.
This raises both v and single landsberg. Shockley and Queisser include a graph showing the overall efficiency as a function of band gap for various values of f.
Shockley and Queisser's work considered the most basic physics only; there are a number of other factors that further reduce the theoretical power. When an electron is ejected through photoexcitation, the atom it was formerly bound to is left with a net positive charge. Under normal conditions, the atom will pull off an electron from single landsberg surrounding atom in order to neutralize itself.
That atom single landsberg then attempt to remove an electron from another atom, and so forth, producing an ionization chain reaction that moves through the cell. Since these can be viewed as the motion of a positive charge, it is useful to refer to them as "holes", a sort of virtual positive electron, single landsberg. Like electrons, holes move around the material, and will be attracted towards a source of electrons.
Normally these are provided through an electrode on the back surface of the cell. Meanwhile, the conduction-band electrons are moving forward towards the electrodes single landsberg the front surface, single landsberg.
For a variety of reasons, holes in silicon move much more slowly than electrons. This means that during the finite time while the electron is moving forward towards the p-n junction, it may meet a slowly single landsberg hole left behind by a previous photoexcitation.
When this occurs, the electron recombines at that atom, and the energy is lost normally through the emission of a photon of that energy, but there are a variety of possible processes.
Recombination single landsberg an upper limit on the rate of single landsberg past a certain rate there are so many holes in motion that new electrons will never make it to the p-n junction, single landsberg.
In brighter light, when it is concentrated by mirrors single landsberg lenses for example, this effect is magnified. Normal silicon cells quickly saturate, while GaAs continue to improve at concentrations as high as times. Recombination between electrons and holes is detrimental in a solar cell, so designers try to minimize it.
However, radiative recombination—when an electron and hole recombine to create a photon that exits the cell into the air—is inevitable, because it is the time-reversed process of light absorption.
Therefore, single landsberg, the Shockley—Queisser calculation takes radiative recombination into account; but it assumes optimistically that there is no other source of recombination. More realistic limits, single landsberg are lower than the Shockley—Queisser limit, can be calculated by taking into account other causes of recombination. These include recombination at defects and grain boundaries.
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