# Solar cell efficiency

Dust often accumulates on the glass of solar modules - seen here as black dots - which reduces the amount of light admitted to the solar cells

Solar cell efficiency refers to the portion of energy in the form of sunlight that can be converted via photovoltaics into electricity.

The efficiency of the solar cells used in a photovoltaic system, in combination with latitude and climate, determines the annual energy output of the system. For example, a solar panel with 20% efficiency and an area of 1 m2 will produce 200 W at Standard Test Conditions, but it can produce more when the sun is high in the sky and will produce less in cloudy conditions and when the sun is low in the sky. In central Colorado, which receives annual insolation of 5.5 kWh/m2/day,[1] such a panel can be expected to produce 440 kWh of energy per year. However, in Michigan, which receives only 3.8 kWh/m2/day,[1] annual energy yield will drop to 280 kWh for the same panel. At more northerly European latitudes, yields are significantly lower: 175 kWh annual energy yield in southern England.[2]

Several factors affect a cell's conversion efficiency value, including its reflectance efficiency, thermodynamic efficiency, charge carrier separation efficiency, and conduction efficiency values.[3] Because these parameters can be difficult to measure directly, other parameters are measured instead, including quantum efficiency, VOC ratio, and fill factor. Reflectance losses are accounted for by the quantum efficiency value, as they affect "external quantum efficiency." Recombination losses are accounted for by the quantum efficiency, VOC ratio, and fill factor values. Resistive losses are predominantly accounted for by the fill factor value, but also contribute to the quantum efficiency and VOC ratio values.

As of December 2014, the world record for solar cell efficiency at 46% was achieved by using multi-junction concentrator solar cells, developed from collaboration efforts of Soitec, CEA-Leti, France together with Fraunhofer ISE, Germany.[4]

## Factors affecting energy conversion efficiency

The factors affecting energy conversion efficiency were expounded in a landmark paper by William Shockley and Hans Queisser in 1961.[5] See Shockley-Queisser limit for more detail.

### Thermodynamic efficiency limit and infinite-stack limit

The Shockley-Queisser limit for the efficiency of a single-junction solar cell under unconcentrated sunlight. This calculated curve uses actual solar spectrum data, and therefore the curve is wiggly from IR absorption bands in the atmosphere. This efficiency limit of ~34% can be exceeded by multijunction solar cells.

If one has a source of heat at temperature Ts and cooler heat sink at temperature Tc, the maximum theoretically possible value for the ratio of work (or electric power) obtained to heat supplied is 1-Tc/Ts, given by a Carnot heat engine. If we take 6000 K for the temperature of the sun and 300 K for ambient conditions on earth, this comes to 95%. In 1981, Alexis de Vos and Herman Pauwels showed that this is achievable with a stack of an infinite number of cells with band gaps ranging from infinity (the first cells encountered by the incoming photons) to zero, with a voltage in each cell very close to the open-circuit voltage, equal to 95% of the band gap of that cell, and with 6000 K blackbody radiation coming from all directions. However, the 95% efficiency thereby achieved means that the electric power is 95% of the net amount of light absorbed – the stack emits radiation as though it were almost at 6000 K, and this radiation has to be subtracted from the incoming radiation when calculating the amount of heat being transferred and the efficiency. They also considered the more relevant problem of maximizing the power output for a stack being illuminated from all directions by 6000 K blackbody radiation. In this case, the voltages must be lowered to less than 95% of the band gap (the percentage is not constant over all the cells). They found that the maximum power was 86.8% of the amount of in-coming radiation. When the in-coming radiation comes only from an area of the sky the size of the sun, the efficiency limit drops to 68.7%.[6]

### Ultimate efficiency

Normal photovoltaic systems however have only one p-n junction and are therefore subject to a lower efficiency limit, called the "ultimate efficiency" by Shockley and Queisser. Photons with an energy below the band gap of the absorber material cannot generate an electron-hole pair, so their energy is not converted to useful output, and only generates heat if absorbed. For photons with an energy above the band gap energy, only a fraction of the energy above the band gap can be converted to useful output. When a photon of greater energy is absorbed, the excess energy above the band gap is converted to kinetic energy of the carrier combination. The excess kinetic energy is converted to heat through phonon interactions as the kinetic energy of the carriers slows to equilibrium velocity. Traditional single-junction cells have a maximum theoretical efficiency of 33.16%.[7]

Solar cells with multiple band gap absorber materials improve efficiency by dividing the solar spectrum into smaller bins where the thermodynamic efficiency limit is higher for each bin.[8]

### Quantum efficiency

Main article: Quantum efficiency

As described above, when a photon is absorbed by a solar cell it can produce an electron-hole pair. One of the carriers may reach the p-n junction and contribute to the current produced by the solar cell; such a carrier is said to be collected. Or, the carriers recombine with no net contribution to cell current.

Quantum efficiency refers to the percentage of photons that are converted to electric current (i.e., collected carriers) when the cell is operated under short circuit conditions. The "external" quantum efficiency of a silicon solar cell includes the effect of optical losses such as transmission and reflection.

In particular, some measurement can be taken to reduce these losses. The reflection losses, which can account for up to 10% of the total incident energy, can be dramatically decreased using a technique called texturization, a light trapping method that modifies the average light path.[9]

Quantum efficiency is most usefully expressed as a spectral measurement (that is, as a function of photon wavelength or energy). Since some wavelengths are absorbed more effectively than others, spectral measurements of quantum efficiency can yield valuable information about the quality of the semiconductor bulk and surfaces. Quantum efficiency alone is not the same as overall energy conversion efficiency, as it does not convey information about the fraction of power that is converted by the solar cell.

### Maximum power point

A solar cell may operate over a wide range of voltages (V) and currents (I). By increasing the resistive load on an irradiated cell continuously from zero (a short circuit) to a very high value (an open circuit) one can determine the maximum power point, the point that maximizes V×I; that is, the load for which the cell can deliver maximum electrical power at that level of irradiation. (The output power is zero in both the short circuit and open circuit extremes).

A high quality, monocrystalline silicon solar cell, at 25 °C cell temperature, may produce 0.60 V open-circuit (VOC). The cell temperature in full sunlight, even with 25 °C air temperature, will probably be close to 45 °C, reducing the open-circuit voltage to 0.55 V per cell. The voltage drops modestly, with this type of cell, until the short-circuit current is approached (ISC). Maximum power (with 45 °C cell temperature) is typically produced with 75% to 80% of the open-circuit voltage (0.43 V in this case) and 90% of the short-circuit current. This output can be up to 70% of the VOC x ISC product. The short-circuit current (ISC) from a cell is nearly proportional to the illumination, while the open-circuit voltage (VOC) may drop only 10% with an 80% drop in illumination. Lower-quality cells have a more rapid drop in voltage with increasing current and could produce only 1/2 VOC at 1/2 ISC. The usable power output could thus drop from 70% of the VOC x ISC product to 50% or even as little as 25%. Vendors who rate their solar cell "power" only as VOC x ISC, without giving load curves, can be seriously distorting their actual performance.

The maximum power point of a photovoltaic varies with incident illumination. For example, accumulation of dust on photovoltaic panels reduces the maximum power point.[10] For systems large enough to justify the extra expense, a maximum power point tracker tracks the instantaneous power by continually measuring the voltage and current (and hence, power transfer), and uses this information to dynamically adjust the load so the maximum power is always transferred, regardless of the variation in lighting.

### Fill factor

Another defining term in the overall behavior of a solar cell is the fill factor (FF). This is the available power at the maximum power point (Pm) divided by the open circuit voltage (VOC) and the short circuit current (ISC):

${\displaystyle FF={\frac {P_{m}}{V_{OC}\times I_{SC}}}={\frac {\eta \times A_{c}\times G}{V_{OC}\times I_{SC}}}.}$

The fill factor is directly affected by the values of the cell's series, shunt resistances and diodes losses. Increasing the shunt resistance (Rsh) and decreasing the series resistance (Rs) lead to a higher fill factor, thus resulting in greater efficiency, and bringing the cell's output power closer to its theoretical maximum.[11]

The Fill factor has a value around 80% for a normal silicon PV cell.

## Comparison

Main article: Photovoltaics

Energy conversion efficiency is measured by dividing the electrical output by the incident light power. Factors influencing output include spectral distribution, spatial distribution of power, temperature, and resistive load. IEC standard 61215 is used to compare the performance of cells and is designed around standard (terrestrial, temperate) temperature and conditions (STC): irradiance of 1 kW/m2, a spectral distribution close to solar radiation through AM (airmass) of 1.5 and a cell temperature 25 °C. The resistive load is varied until the peak or maximum power point (MPP) is achieved. The power at this point is recorded as Watt-peak (Wp). The same standard is used for measuring the power and efficiency of PV modules.

Air mass affects output. In space, where there is no atmosphere, the spectrum of the sun is relatively unfiltered. However, on earth, air filters the incoming light, changing the solar spectrum. The filtering effect ranges from Air Mass 0 (AM0) in space, to approximately Air Mass 1.5 on Earth. Multiplying the spectral differences by the quantum efficiency of the solar cell in question yields the efficiency. Terrestrial efficiencies typically are greater than space efficiencies. For example, a silicon solar cell in space might have an efficiency of 14% at AM0, but 16% on earth at AM 1.5. Note, however, that incident photons in space carry considerably more energy, so the solar cell might produce considerably more power in space, despite the lower efficiency as indicated by reduced percentage of the total incident energy captured.

Reported timeline of solar cell energy conversion efficiencies since 1976 (National Renewable Energy Laboratory)

Solar cell efficiencies vary from 6% for amorphous silicon-based solar cells to 44.0% with multiple-junction production cells and 44.4% with multiple dies assembled into a hybrid package.[12][13] Solar cell energy conversion efficiencies for commercially available multicrystalline Si solar cells are around 14-19%.[14] The highest efficiency cells have not always been the most economical — for example a 30% efficient multijunction cell based on exotic materials such as gallium arsenide or indium selenide produced at low volume might well cost one hundred times as much as an 8% efficient amorphous silicon cell in mass production, while delivering only about four times the output.

However, there is a way to "boost" solar power. By increasing the light intensity, typically photogenerated carriers are increased, increasing efficiency by up to 15%. These so-called "concentrator systems" have only begun to become cost-competitive as a result of the development of high efficiency GaAs cells. The increase in intensity is typically accomplished by using concentrating optics. A typical concentrator system may use a light intensity 6-400 times the sun, and increase the efficiency of a one sun GaAs cell from 31% at AM 1.5 to 35%.

A common method used to express economic costs is to calculate a price per delivered kilowatt-hour (kWh). The solar cell efficiency in combination with the available irradiation has a major influence on the costs, but generally speaking the overall system efficiency is important. Commercially available solar cells (as of 2006) reached system efficiencies between 5 and 19%.

Undoped crystalline silicon devices are approaching the theoretical limiting efficiency of 29.4%[15] In 2014, efficiency of 25.6% was achieved in crystalline cells that place both positive and negative contacts on the back of the cell and that cover the wafer's front and back with thin films of silicon.[16]

### Energy payback

The energy payback time is defined as the recovery time required for generating the energy spent for manufacturing a modern photovoltaic module. In 2008 it was estimated to be from 1 to 4 years[17][18] depending on the module type and location. With a typical lifetime of 20 to 30 years, this means that, modern solar cells would be net energy producers, i.e. they would generate more energy over their lifetime than the energy expended in producing them.[17][19][20] Generally, thin-film technologies—despite having comparatively low conversion efficiencies—achieve significantly shorter energy payback times than conventional systems (often < 1 year).[21]

A study published in 2013 which the existing literature found that energy payback time was between 0.75 and 3.5 years with thin film cells being at the lower end and multi-si-cells having a payback time of 1.5-2.6 years.[22] A 2015 review assessed the energy payback time and EROI of solar photovoltaics. In this meta study, which uses an insolation of 1700 kWh/m2/year and a system lifetime of 30 years, mean harmonized EROIs between 8.7 and 34.2 were found. Mean harmonized energy payback time varied from 1.0 to 4.1 years.[23] Crystalline silicon devices achieve on average an energy payback period of 2 years.[17][24]

Like any other technology, solar cell manufacture is dependent on and presupposes the existence of a complex global industrial manufacturing system. This comprises not only the fabrication systems typically accounted for in estimates of manufacturing energy, but the contingent mining, refining and global transportation systems, as well as other energy intensive critical support systems including finance, information, and security systems. The uncertainty of that energy component confers uncertainty on any estimate of payback times derived from that estimate, considered by some to be significant.[25]

## Technical methods of improving efficiency

### Promoting light scattering in the visible spectrum

By lining the light receiving surface of the cell with nano-sized metallic studs, the efficiency of the cell can be substantially increased, as the light reflects off these studs at an oblique angle to the cell, increasing the length of the path the light takes through the cell, thereby increasing the number of photons absorbed by the cell, and so also the amount of current generated.[26]

The main materials used for the nano-studs are silver, gold, and aluminium. However, gold and silver are not very efficient, as they absorb much of the light in the visible spectrum, which contains most of the energy present in sunlight, reducing the amount of light reaching the cell.[26] Aluminium, on the other hand, absorbs only ultraviolet radiation, and reflects both visible and infra-red light, so energy loss is minimized on that front. Aluminium is therefore capable of increasing the efficiency of the cell by up to 22% (in lab conditions).[27]

An increase in solar cell temperature of around 1 °C leads to a decrease in efficiency of about 0.45%.To prevent decreased efficiency due to heating, a visibly transparent silica crystal layer can be applied to a solar panel. The silica layer acts as a thermal black body which emits heat as infrared radiation into space cooling the cell by up to 13 °C.[28]

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