Single-junction solar cells have a maximum theoretical efficiency of 33.16%, the Shockley-Queisser limit. But there are work-arounds that permit solar array designers to surpass that limit on a square-foot basis.
The maximum solar conversion efficiency of around 33.7% happens at a 1.34 eV band gap and is subject to several assumptions. By way of review, band gap in a solid is the energy range in which there are no electronic states. It is the energy difference, in electron volts, between the top of the valence band and the bottom of the conduction band. It is also the energy required–for example, by the impact of a photon–to convert a valence electron to a conduction electron, which then becomes free to move within the crystal lattice of the cell, becoming an electrical charge carrier.
Insulators, such as diamond, have large band gaps (lots of energy required), while semiconductors have intermediate band gaps (moderate energy required). Conductors have small or zero band gaps because the valence and conductor bands overlap.
In a solar voltaic cell, the optical band gap determines the portion of the solar spectrum the cell can absorb. To be converted to electrical energy in a solar cell, the radiation cannot be reflected and it cannot be transmitted, but it must be absorbed by the photovoltaic material. When a photon strikes an orbiting electron, it leaves the atom and becomes part of the electrical output of the cell, provided it is not captured by a positive ion in a process known as recombination, which reduces efficiency. A semiconductor can absorb photons having greater energy than the material band gap. Moreover, the energy of an electron-hole pair produced by a photon impact is equal to the band gap.
When an electron is removed from a silicon (or other) atom, that atom becomes a positive ion and it seeks to capture an electron from a neighboring atom to return to its preferred, neutral state. If it succeeds, that neighboring atom becomes a positive ion and in turn attempts to capture an electron, creating in the process a new ion. So the process continuous, resulting in a great number of ionization chain reactions. This is known as recombination, and it reduces solar cell efficiency in silicon by approximately by approximately 10%. The Shockley-Queisser limit includes this factor as well as a related phenomenon, known as radiative recombination. Radiative recombination arises when an electron and a positive ion recombine, creating a photon that leaves the cell. The bottom line is that there is one less electron, which must be deducted from the solar cell electrical output.
Any type of recombination degrades efficiency. There are other factors which also prevent cells from operating at maximum efficiency. For example, even with good tracking, the solar panels may not be perfectly perpendicular to the solar radiation. Also, the wire grid on the front side of the cells blocks a portion of the light. If the topside wire grid is made up of thinner conductors to reduce this masking effect, there is greater resistive loss. An improved topside grid is comprised of conductors having a rectangular cross section, but this approach works best only when the solar radiation is perpendicular to the cell so there’s no shadowing.
The Shockley-Queisser (SQ) calculation assumes:
Only a single electron-hole combination is excited per photon
Thermal relaxation of the electron-hole energy exceeds that of the band gap.
Illumination is from non-concentrated sunlight. (If mirrors are used to multiply light intensity, efficiency doesn’t rise. That percentage is instead applied to an amount of light greater than the energy contained in clear conditions, roughly 1,000 W/m2.
The SQ equation is usually given as
η=ts u(xg) v(f, xc, xg) m(vxg/xc)
Here ts = the fraction of photons above the band-gap energy falling on the cell per unit area that generate an electron-hole pair; u = an efficiency factor associated with spectrum losses; xg = the ratio of the bandgap voltage to the voltage equivalent of the temperature of the sun; v = the ratio of band-gap voltage to open-circuit voltage; f = a function of the solid angle of the sun divided by π; xc = the ratio of the voltage equivalent of the temperature of the cell to the voltage equivalent of the temperature of the sun; and m = an impedance matching factor.
A number of approaches are in use as a means to hit efficiencies exceeding that delineated by the SQ limit. An example is the multijunction, or tandem photovoltaic cell. It consists of two or more p-n junctions, each tuned to a specific frequency band. This technique addresses the problem that a material with a single band gap cannot absorb sunlight below the band gap or far above it. Generally, a high-band-gap cell sits at the top of the structure. It absorbs a portion of the lower-energy, shorter-wavelength light, allowing all other wavelengths to pass through. Next is a lower-band-gap cell which absorbs a portion of the longer-wavelength radiation. The complete cell may contain as many as four layers. A two-layer cell can attain 42% efficiency, a three-layer cell 49% efficiency. Hypothetically, with an infinite number of layers, the Shockley-Queisser limit would be 68%.
The usual configuration for tandem cells is blue light sensitivity on top, yellow sensitivity in the middle and red sensitivity on the bottom. Because the semiconductors must have discrete band gaps, these cells generally employ gallium arsenide as opposed to silicon, germanium for the red portion of the spectrum, GaAs for yellow and GaInP2 for blue. Trouble is, the processing steps involved make these cells expensive. This technique is usually restricted to aerospace applications where performance and a favorable power-to-weight ratio outweighs cost. The expense can be mitigated to some extent by using low-efficiency materials to build moderate efficiency three-junction amorphous silicon solar cells.
Solar cells that use quantum dots rather than traditional photovoltaic materials such as silicon, copper, indium, gallium selenide, or cadmium telluride have far exceeded the Shockley-Queisser limit. Quantum dots are extremely small semiconductors occupying only a few nanometers. They have optical and electronic properties that differ from larger particles as described in quantum mechanics. They are produced in great quantities and used in many applications because they are easy to manufacture and relatively inexpensive to implement.
Quantum dots change their size and thus band gaps, and they can be tuned to many energy levels because band gap depends upon size. This property permits them to operate in large portions of the spectrum as required in tandem applications. Some quantum dots are semiconductors that are smaller than the Exciton Bohr radius. This physical constant is equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. These virtual atoms possess finite electron energies that can be tuned by changing their size and band gap. Single-junction solar cells have used quantum technology to access infrared frequencies, otherwise difficult to accomplish in conventional cells. This suggests that in the future we will be able to harvest electrical power using quantum dots by simply lowering ambient temperatures.
Quantum dots, despite the imposing name, are relatively easy to produce using spin coating, spray-on or roll-printing methods, contributing to lower cost and the prospect of large-scale construction.