Actual Calculation of Solar Cell Efficiencies

  • Takashi KitaEmail author
  • Yukihiro Harada
  • Shigeo Asahi
Part of the Green Energy and Technology book series (GREEN)


In Chap.  5, we derived the single-junction solar cell conversion efficiency within the framework of the detailed balance theory and computed the solar spectrum by employing Planck’s law for black-body radiation. As explained in Sect.  2.2, the solar spectrum that passes the atmosphere differs according to the amount of air passed. This amount can be expressed as air mass (AM). In this chapter, we do not rely on the black-body radiation for the solar spectrum, but employ the actual spectral data for the sunlight that reaches the Earth after passing the atmosphere. With this data, we calculate the conversion efficiencies of several different solar cell structures. We first recalculate the conversion efficiency of the single-junction solar cell in Sect. 6.1 by using the real solar spectrum. In Sect. 6.2, we determine the conversion efficiency of a solar cell under concentrated sunlight, which can be obtained, for example, by using a lens. Additionally, in Sects. 6.36.6 we discuss four selected solar cell structures that are recently attracting attention as novel types of solar cells with the ability to overcome the S–Q limit. To exceed the S–Q limit means that the transmission and thermalization losses, which we declared as “being unavoidable,” have to “be avoided somehow” by using novel approaches. For the reduction of the losses and conversion of the sunlight into electrical power to the best extent possible, we can either increase the wavelength range that is employed by the solar cell for conversion into electrical power, or the opposite, and we can reshape the solar spectrum itself in such a way that it can be efficiently converted into electrical power by the solar cell. As examples for the first-mentioned approach, we discuss the multi-junction solar cell (which can also be called tandem solar cell) in Sect. 6.3 and the intermediate-band solar cell in Sect. 6.4. Multi-junction solar cells comprise a multilayer structure where each of the stacked layers is a semiconductor junction with different Eg. This method enables capturing the light transmitted through one solar cell by another solar cell in the layer below. Therefore, the light that would usually be lost through transmission can be used for electricity generation, and this allows us to exceed the S–Q limit of the single junction. This solar cell architecture has already been practically implemented, and the multi-junction type is the current world record holder in terms of solar cell performance. Unfortunately, the series connection between the junctions constitutes a drawback for the multi-junction solar cells. The tandem solar cells consist of stacked junctions that are serially connected. Therefore, the electricity generation is already completely suppressed if one of the stacked junctions does not operate. For example, a certain spectral part of the light may hardly reach the solar cell due to the scattering and absorption in clouds on a cloudy day. If due to this the electricity generation of any solar cell in the stack drops, the performance of the whole device is affected because the current that flows through the directly affected cell is reduced and becomes the bottleneck of the whole device, even if the solar cells in the other layers work fine. On the other hand, the intermediate-band solar cell has attracted attention as a solar cell architecture that promises high conversion efficiencies and can also lift the restrictions imposed by the series connection of the multi-junction tandem solar cells. This architecture reduces the transmission losses by implementing a new band (the so-called intermediate band) within the band gap of the solar cell. Because the direct absorption of the light via a transition between the conduction and the valence bands (a so-called interband transition) occurs in parallel with the stepwise absorption via the intermediate band, the intermediate-band solar cell’s electricity generation cannot be completely suppressed under clouded conditions as was the case for the multi-junction solar cells. In the intermediate-band solar cell, by absorbing a below-gap photon, an electron transits from the valence band to the intermediate band. Upon absorbing another below-gap photon, the electron is further excited into the conduction band. There transitions widely cover the solar spectrum. This two-step excitation (two-step photon up-conversion) process following the absorption of two below-gap photons produces additional photocurrent without degrading the photovoltage. Such two-step photoexcitation is known to occur at heterointerfaces. In Sect. 6.5, we deal with a solar cell containing a heterointerface in the intrinsic layer so-called two-step photon up-conversion solar cell. The conversion efficiency of the solar cell utilizing interband and intraband transitions strongly depends on the absorptivity of these transitions. Detailed influences of the absorptivity of photovoltaic materials on the conversion efficiency are also discussed. Section 6.6 discusses one example for the reduction of losses by altering the solar spectrum. To reduce the transmission losses, it is necessary to convert the light in the long-wavelength region of the solar spectrum into light with shorter wavelengths. Similarly, to reduce losses through thermalization, it is necessary to convert the light in the short-wavelength region of the solar spectrum into light with longer wavelengths. We analyze how much the conversion efficiency can be improved by down-converting the short-wavelength light (high photon energies) to long-wavelength light (small photon energies). Besides, the influences of changing weather conditions on the conversion efficiency of various types of solar cells are introduced in detail in Sect. 6.7. Up to Sect. 6.7, we proceed to discuss the solar cell at a constant temperature of 300 K. However, since concentration of sunlight is an important technique to enhance conversion efficiencies, the influence of the temperature has to be investigated. Due to the strong concentration of sunlight, the temperature of the concentrator solar cell device increases. If the temperature increases, the semiconductor band gap becomes smaller and furthermore, a higher the electron–hole recombination rate (stronger black-body radiation) is observed as explained in Sect.  4.2; this causes a decrease in the conversion efficiency. In Sect. 6.8, we analyze the change in the single-junction solar cell efficiency that occurs upon a change in the solar cell temperature. The solar cell is the photovoltaic device used as a solar energy converter. When indoor light such as white light-emitting diode (LED) is harvested, the optimized energy structure of the photovoltaic materials is different from the results obtained for the sunlight. We touch the energy conversion efficiency of indoor photovoltaic cells in Sect. 6.9.


Single-junction solar cell Concentrator solar cell Multi-junction solar cell Intermediate-band solar cell Two-step photon up-conversion solar cell Spectral converter Actual solar spectra 


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringKobe UniversityKobeJapan

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