The upper limit on the theoretical efficiency of a single-junction solar cell. Balancing the transmission of light below the band gap against thermalization losses, it reaches a maximum of about 33% at about 1.34 eV under terrestrial sunlight.
Japanese name: ショックレー・クワイサー限界
Shockley–Queisser limit appears in 1 practice question across 1 topic, including Battery and energy materials.
Field: Battery and energy materials
In 1961, Shockley and Queisser treated a solar cell as a body that receives sunlight and also emits light according to its own temperature, and derived the upper limit of efficiency from the balance of light in and out (detailed balance). The assumptions were that every photon with energy above the band gap is absorbed and creates one electron–hole pair, that the only recombination is radiative recombination, which emits light, and that carriers instantly cool to the band edges. The important point is that even an ideal cell, with no defect recombination or resistive losses, retains the unavoidable loss of radiative recombination.
Photons with energy below the band gap Eg are not absorbed and are lost by transmission. Photons above Eg are absorbed, but their excess energy is lost as heat while the electrons fall to the band edge (thermalization). For example, when a 2.5 eV photon is absorbed by a 1.1 eV gap, 1.4 eV becomes heat. A smaller gap absorbs more light but lowers the voltage, while a larger gap raises the voltage but absorbs less light. Balancing these, the maximum for terrestrial sunlight (AM1.5) is about 33% at about 1.34 eV.
The Shockley–Queisser limit is not an upper bound on all conversion of sunlight, like the Carnot efficiency of heat engines. It is the limit under assumptions such as a single junction, one carrier pair per photon and no concentration, and it can be exceeded if those assumptions are dropped. Multijunction solar cells, which stack cells with different gaps, absorb each part of the spectrum in the layer best suited to it and reduce thermalization, and efficiencies well above 40% have been reported under concentration. Also, silicon (1.12 eV) lies close to the maximum of the limit, but as an indirect-gap material it absorbs light weakly and needs a thick absorber, so unavoidable Auger recombination becomes the main loss, and its practical limit is estimated at about 29%.
The limit curve serves as a yardstick for evaluating new solar cell materials. Many perovskite solar cells use materials with band gaps of about 1.5–1.6 eV because that range is close to the maximum of the limit. Comparing a real cell's open-circuit voltage, short-circuit current and fill factor with the limiting values for the same gap shows where the losses lie. A shortfall in open-circuit voltage in particular indicates a large amount of non-radiative recombination. Tandem cells that stack a wide-gap perovskite on silicon are being developed with the aim of exceeding the single-junction limit.
Answer: A. A small band gap gives a low voltage and loses excess energy as heat, while a large one leaves more photons unabsorbed
A photon is absorbed only when its energy is at least the band gap Eg, and the energy in excess of Eg is handed to the lattice as heat by the carriers (thermalization loss). In addition, the open-circuit voltage cannot exceed Eg/q. With a small Eg more photons are absorbed but less energy can be extracted per photon; with a large Eg the voltage is higher, but photons with energy below Eg are not absorbed and pass through. Balancing these, the Shockley–Queisser theoretical efficiency under standard terrestrial sunlight (AM1.5) is high, about 32–33%, over the range of about 1.1–1.4 eV, with a maximum of about 33% at about 1.34 eV. The statement that a larger Eg increases absorption is backward. The intensity of sunlight varies greatly with wavelength and is not constant.
For the terrestrial solar spectrum (AM1.5), the maximum is about 33% at a band gap of about 1.34 eV. The original 1961 paper treated the sun as a 6000 K blackbody and gave about 30% at about 1.1 eV.
Because they stack cells with different band gaps, absorbing short-wavelength light in the upper layer with a large gap and long-wavelength light in the lower layer with a small gap, which reduces thermalization and transmission losses at the same time.
Because stronger light increases the current proportionally, and the open-circuit voltage also rises with the logarithm of the light intensity, so efficiency increases. At the ideal maximum concentration, the limit even for a single junction rises to about 40%.
Balancing these, the Shockley–Queisser theoretical efficiency under standard terrestrial sunlight (AM1.5) is high, about 32–33%, over the range of about 1.1–1.4 eV, with a maximum of about 33% at about 1.34 eV.
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