# Solar cell efficiency

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

Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion efficiency (η) of a solar cell is the percentage of the solar energy to which the cell is exposed that is converted into electrical energy.[1] This is calculated by dividing a cell's power output (in watts) at its maximum power point (Pm) by the irradiance (input light), G, in W/m2 and the surface area of the solar cell (Ac in m2).

$\eta = \frac{P_{m}}{G \times A_c}$

By convention, solar cell efficiencies are measured under standard test conditions (STC) unless stated otherwise. STC specifies a temperature of 25 °C and an irradiance (G) of 1000 W/m2 with an air mass 1.5 (AM1.5) spectrum. These conditions correspond to a clear day with sunlight incident upon a sun-facing 37°-tilted surface with the sun at an angle of 41.81° above the horizon.[2][3] This represents solar noon near the spring and autumn equinoxes in the continental United States with surface of the cell aimed directly at the sun. Under these test conditions a solar cell of 20% efficiency with a 100 cm2 ( (10 cm)2 ) surface area would produce 2.0 W.

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 STC, 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 2200 kWh/m²,[4] such a panel can be expected to produce 440 kWh of energy per year. However, in Michigan, which receives only 1400 kWh/m²/yr,[4] 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.[5]

Several factors affect a cell's conversion efficiency value, including its reflectance efficiency, thermodynamic efficiency, charge carrier separation efficiency, and conduction efficiency values.[1] 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 September 2013, the highest efficiencies have been achieved by using multiple junction cells at high solar concentrations (44.7% by the Fraunhofer ISE, Soitec, CEA-Leti and the Helmholtz-Zentrum Berlin).[6]

## Factors affecting energy conversion efficiency

### Thermodynamic efficiency 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.

The maximum theoretically possible conversion efficiency for sunlight is given by a Carnot heat engine operating between the temperature of the Sun (5800K) and ambient conditions on earth (300K), which is 95%. The conversion efficiency for sunlight, while extracting maximum work, is 86% due to the entropy of the photons emitted by the sun's surface.[7]

However, solar cells operate as quantum energy conversion devices, and are therefore subject to the "thermodynamic efficiency limit". Photons with an energy below the band gap of the absorber material cannot generate a hole-electron pair, and 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.

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. If some of these losses can be recaptured by other portions of the solar cell array (for example via oblique angles of incidence) the aggregate external quantum efficiency of the system may be increased despite a lower internal quantum efficiency. However, it is often useful to look at the quantum efficiency of the light left after the reflected and transmitted light has been lost. "Internal" quantum efficiency refers to the efficiency with which photons that are not reflected or transmitted out of the cell can generate collectable carriers

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.[9] 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):

$FF = \frac{P_{m}}{V_{OC} \times I_{SC}} = \frac{\eta \times A_c \times E}{V_{OC} \times I_{SC}}.$

The fill factor is directly affected by the values of the cell's series and shunt resistances. 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.[10]

## 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.[11][12] Solar cell energy conversion efficiencies for commercially available multicrystalline Si solar cells are around 14-19%.[13] 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%[14] 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.[15]

### 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[16][17] 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.[16][18][19] Generally, thin-film technologies—despite having comparatively low conversion efficiencies—achieve significantly shorter energy payback times than conventional systems (often < 1 year).[20]

Crystalline silicon devices achieve on average an energy payback period of 2 years.[16][21]

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.[22]

## References

1. ^ a b "Photovoltaic Cell Conversion Efficiency Basics". U.S. Department of Energy. Retrieved 6 Sep 2014.
2. ^ ASTM G 173-03, "Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface," ASTM International, 2003.
3. ^ "Solar Spectral Irradiance: Air Mass 1.5". National Renewable Energy Laboratory. Retrieved 12 December 2007.
4. ^ a b Photovoltaic Solar Resource of the United States, http://www.nrel.gov/gis/images/map_pv_national_lo-res.jpg
5. ^ Solar photovoltaics: data from a 25-m2 array in Cambridgeshire in 2006, http://www.inference.phy.cam.ac.uk/withouthotair/c6/page_40.shtml
6. ^ "World record solar cell with 44.7% efficiency". ScienceDaily. Retrieved 2014-06-22.
7. ^ A. De Vos and H. Pauwels (1981). "On the Thermodynamic Limit of Photovoltaic Energy Conversion". Appl. Phys. 25: 119–125. Bibcode:1981ApPhy..25..119D. doi:10.1007/BF00901283.
8. ^ Cheng-Hsiao Wu and Richard Williams (1983). "Limiting efficiencies for multiple energy-gap quantum devices". J. Appl. Phys. 54: 6721. Bibcode:1983JAP....54.6721W. doi:10.1063/1.331859.
9. ^ A. Molki (2010). "Dust affects solar-cell efficiency". Physics Education 45: 456–458. Bibcode:2010PhyEd..45..456M. doi:10.1088/0031-9120/45/5/F03.
10. ^ Jenny Nelson (2003). The Physics of Solar Cells. Imperial College Press. ISBN 978-1-86094-340-9.
11. ^ "Solar Junction Breaks Its Own CPV Conversion Efficiency Record". 2013-12-18. Retrieved 2013-12-18.
12. ^ "Solar Cell Efficiency World Record Set By Sharp — 44.4%". 28 July 2013. Retrieved 28 July 2013.
13. ^
14. ^ A. Richter, M. Hermle, S.W. Glunz (October 2013). "Reassessment of the limiting efficiency for crystalline silicon solar cells". IEEE Journal of Photovoltaics 3 (4): 1184–1191. doi:10.1109/JPHOTOV.2013.2270351.
15. ^ Bullis, Kevin (2014-06-13). "A Record-Breaking Solar Cell | MIT Technology Review". Technologyreview.com. Retrieved 2014-06-22.
16. ^ a b c "What is the Energy Payback for PV?" (PDF). Retrieved 20 December 2008.
17. ^ M. Ito, K. Kato, K. Komoto et al. (2008). "A comparative study on cost and life-cycle analysis for 100 MW very large-scale PV (VLS-PV) systems in deserts using m-Si, a-Si, CdTe, and CIS modules". Progress in Photovoltaics: Research and Applications 16: 17–30. doi:10.1002/pip.770.
18. ^ "Net Energy Analysis For Sustainable Energy Production From Silicon Based Solar Cells" (PDF). Retrieved 2011-09-13.
19. ^ Corkish, Richard (1997). "Can Solar Cells Ever Recapture the Energy Invested in their Manufacture?". Solar Progress 18 (2): 16–17.
20. ^ K. L. Chopra, P. D. Paulson, and V. Dutta (2004). "Thin-film solar cells: An overview Progress in Photovoltaics". Research and Applications 12: 69–92. doi:10.1002/pip.541.
21. ^ "Highest silicon solar cell efficiency ever reached". ScienceDaily. 24 October 2008. Retrieved 9 December 2009.
22. ^ Trainer, FE (2007) "Renewable Energy Cannot Sustain a Consumer Society"