Detailed balance limit of efficiency of pn junction solar cells

Detailed balance offers an approach to calculate the maximum effectiveness of photovoltaic tools. Originally the method was proposed by Shockley and also Queisser in 1961 1. An extended version was publimelted in 1984 by Tiedje et al. 2.

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Detailed balance in its most basic and also most prevalent implementation renders several fundamental assumptions:

The mobility is infinite, enabling arsenal of carriers no issue where they are produced.Complete absorption of all photons over the band also gap.

The calculations for in-depth balance calculations involve calculating the particle flux for various configurations of the Plank’s equation. The basic create of the equation is:

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The general strategy is to calculate the absorption flux and also the flux emitted from the solar cell. The difference between these two (multiplied by q) is the existing from the solar cell.

Absorption flux

The absorption consists of 2 parts; one from the sun and the various other from the various other areas of the skies. Under maximum concentration, the optics renders it such that the whole bordering of the solar cell is illuminated by radiation of the same temperature of the sun. Under conditions other than maximum concentration, one percentage of the skies (shown in yellow below) is illuminated from the sunlight, and also the remainder is illuminated from a radiation source with the same temperature as the Earth. The maximum concentration is calculated based upon the size of the sun’s disc in the skies and is provided by 46,300.

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Schematic depiction of approximations used in detailed balance. On the left picture light is built up from the entire hemispright here which corresponds to maximum concentration. For reduced or no concentration the Sun have the right to be seen as an arc giving lower pshort article flux.

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The absorption from the sun is given by:

φsunEG,∞,0,Tsun=2πh3c2∫EG∞E2expEkTsun-1dE

And the absorption from the babsence body radiation of the earth is:

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The total absorption of the solar cell is:

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Emission flux

The emission from the solar cell relies on the quasi-Fermi level separation (μ) of the solar cell. Under short circuit conditions, m is zero. The emission is calculated by:

φ2EG,∞,μ,TEarth=2πh3c2∫EG∞E2expE-μkTEarth-1dE

Calculation of performance for a fixed Eg and also babsence body

The power from the solar cell depends on the band gap and on the quasi-Fermi level separation. For a offered band gap, the quasi-Fermi level separation have to be differed to uncover the maximum power suggest, i.e., where

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is at a maximum. This is done by varying m from 0 to cshed to the open circuit condition (wbelow φ1 = φ2), and uncover where the power is at a maximum.

The effectiveness is then defined as:

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Efficiency as a role of band gap

To discover the performance as a duty of band gap, the over procedure is recurring for each band also gap. There is an selection of bandgaps for the optimum cell performance as displayed in the graph below.

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Limiting solar cell performance as a role of the material bandgap for one-sun illumicountry. The calculations assume that the only recombicountry is radiative. In actual devices the efficiencies are lower due to other recombicountry mechanisms and losses in parasitic resistances.

AM1.5 Spectrum

To find the effectiveness under an AM1.5 spectra (or other measured spectra), φ1 is reinserted by the summation of the photon flux for energies above the band gap, and also the power from the sun is replaced by the summation of the power in the measured spectra.


1. Introduction2. Properties of Sunlight3. Semiconductors & Junctions4. Solar Cell Operation5. Deauthorize of Silicon Cells6. Manufacturing Si Cells7. Modules and Arrays8. Characterization9. Material Properties10. Batteries11. Appendices